I don't know the talk, but it is certainly possible, in theory at least, to "drive into orbit", for instance, if you use a magnetically elevated track.

This is the idea of  Startram

It's an idea for a maglev acceleration of humans to orbital velocities. It would launch from 0 to 8 km/ second over at least 1000 kms

The track is suspended by magnetic levitation which is easily strong enough to hold it up, they say. It uses only present day materials.

To find out more, see  Startram - for details Maglev Launch: Ultra Low Cost Ultra/High Volume Access to Space for Cargo and Humans

You could also use similar technology to just fire things out of a gun, a "rail gun" which could be electrically powered - but that needs too much acceleration to be practical for humans.

Would work for the likes of fuel or water and has been studied. The authors of the Star Tram proposal suggest that you'd begin with much smaller scale 1 kilometer maglevs built into the side of a mountain, for sending fuel and water to orbit.

For a 1 km gun, which you could quite possibly build as a tunnel through a mountain, to accelerate to 8 km / s to get into LEO, then that's 6,500 g. Which the sorts of electronics designed for ballistic missiles could cope with, so you could send rockets into space with fuel or water in that way using electricity.

That could be a game changer technology even if you don't ever manage to send humans into orbit in the same way. To have low cost consumables in low Earth orbit supplied from Earth, fuel and water.

SPACE ELEVATOR

If you have a space elevator, which we may have in the future, can just drive into space along the elevator using power supplied from a power plant at the foot of the elevator. If you could build a structure that goes all the way into orbit, you can do that.

However, the space elevator which requires materials that seem possible in theory but don't exist yet (like flawless long carbon nanotubes etc). Some think we may have such materials in the near future, even perhaps, within a decade or two.

There are many other issues with the space elevator idea and a whole community of enthusiasts and engineers exploring the ideas, with a 2 millin dollar Google X-prize for certain key developments along the way and regular competitions where the competitors attempt to better each other at various challenges such as beaming power to the climber, or stronger materials for the elevator etc. See The Spaceward Foundation

Here is a recent BBC story about the idea, which incidentally also mentions Elon Musk's ideas on the subject.

Should we give up on the dream of space elevators?

SUPPLYING POWER FROM THE GROUND TO THE RISING SPACECRAFT E.G. WITH LASERS

You can also use lasers to send something into orbit, or other ways of supplying power from the ground.

Lightcraft

IDEAS THAT USE ELECTRICITY TO REDUCE THE AMOUNT OF FUEL NEEDED

In theory an ion thruster would also work, not pure electricity, but about a tenth of the amount of fuel. But so far they use small amounts of fuel and are low thrust and nobody knows of any way to propel hundreds of kilograms of fuel per second using an ion thruster.

If you had any way to directly convert matter to energy, then a photon thruster would be the best solution, wouldn't use much mass, just lots of power. But we don't know of any way to do that.

AIRSHIPS TO ORBIT - COMBINING ELECTRICAL PROPULSION WITH A LIFTING GAS

There's also use of hydrogen and helium balloons however. Lift from Earth surface to a platform in the stratosphere.

Change to much larger balloons, kilometer scale, which gradually accelerate to orbit using ion thrusters. This idea does use some reaction mass, but mainly uses hydrogen or helium as a lifting gas to get to orbit, is electrically powered and gets you all the way to orbit with very little power and only a tiny amount of reaction mass, which is used to slowly accelerate over a period of several days in the near vacuum conditions well above what we normally think of as the atmosphere.

The thing is that a near vacuum of hydrogen or helium can still float in another near vacuum of a heavier gas such as nitrogen (say). Even if there are only a few atoms per cubic centimeter, it would still give you a lifting force.

Even in a near vacuum, a tiny fraction of a percent of one atmosphere, hydrogen or helium still works as a lifting gas. Trap a region of hydrogen or helium inside huge kilometer scale balloons - and it will still supply lift and lift you further and further up into the atmosphere. Until the air is so thin, you can acelerate to faster than the local speed of sound with no ill effects. One of the early Echo satellite balloons survived a ballistic hops in the very high atmosphere at well over the speed of sound without getting destroyed (not during the hop, only at the end of it), so it doesn't seem that travel faster than the speed of sound at such heights would destroy the balloon, which is the main criticism usually made of their idea. The director of the project doesn't see that as their main challenge.

This idea is being explored by JP Aerospace who plan to make ordinary airships that would rise to orbital platforms at 200,000 feet - so that's 60 km, in the mesosphere - above the stratosphere, near vacuum conditions. Then passengers would transfer to the larger orbital airships to go into orbit.

REDUCING REACTION MASS BY AIR BREATHING

Also, this is not electricity, but just to say, in response to some who think that conventional rocketry is the only game in town - that you can also reduce the reaction mass hugely by using air breathing spacecraft such as Skylon, which is under active development in the UK with the very innovative engine passing all the tests so far. If it continues to fulfill the promise it has shown so far, it may see flight in the 2020s. It's being supported to the tune of many millions of pounds on going research in the UK.

And there are several other ideas being pursued.

In short, SpaceX and other conventional rocket companies are pursuing just one of many ideas being investigated.

They are at the head of the game at present of course, the only way we can get into orbit is through chemical rockets. But looking somewhat further into the future, like a few decades, there are other possible technologies on the horizon, so room for some surprises to come in the future.

For more on this, with other examples of some of the ideas under investigation or suggested in the past, see Projects To Get To Space As Easily As We Cross Oceans - A Million Flights A Year Perhaps - Will We Be Ready?

WHY THERE IS NOTHING TO PUSH AGAINST ACCORDING TO CURRENT UNDERSTANDING

I see the question has just been edited so answering the new version.

No you can't "push against gravity" like you can with water or air Not with present day understanding anyway. The idea of a medium in between the planets, the "ether" was disproved by the Michelson–Morley experiment , This shows there is no "aether" for light to move through, so nothing to push against.

Then the development of special relativity, and then general relativity made the situation even clearer. Whether or not those are final theories is another matter, we know that they are incomplete. But there is no support at all at present for any kind of medium like water or air that you could push against or use for support like you could for a boat or a plane. There could be - back in the nineteenth century what you say would seem quite plausible, but according to modern physics, and many experiments like this, there is not.

What they did is to compare the speed of light in two directions at right angles to each other, and they saw no difference at all. This proved that there is no medium that light is moving through, because if there was, the speed would vary depending on the direction Earth is moving relative to the medium.

The alternatives to rockets work by using the air for propulsion, or by using power supplied from below and propulsion with very high speed exhaust, or by building a physical track most of the way into space and maglev acceleration along it. For that matter you can also fire matter into space using a very powerful gun - then there is no need for propulsion at all once it leaves the nozzle except minor adjustments to get into orbit, you have plenty of delta v if you leave with enough speed and can "punch your way" through the atmosphere, or you exit the nozzle well above the thickness of the Earth's atmosphere. That's basically the idea behind maglev.

For a situation that makes this clear, if you want to leave the surface of the Moon, as there is no atmosphere, the only possibilities there are a rocket motor (which can be far smaller because of the Moon's lower gravity), or maglev - basically the gun + nozzle idea - or physically building a track into orbit, as a space elevator, which is actually practical for the Moon with present day materials but very expensive. Or some combination of those. You can't get into orbit by "pushing against gravity".

That's with present day science.

For the future, there's the idea of the EM Drive, which is a bit like what you are talking about.  In the probably unlikely event that it turned out to work and also turned out to be able to produce huge levels of thrust, it could do what you want. I don't think it is necessarily nonsense. Yes it defies conservation of energy and momentum - but any radically new idea is going to do that until you figure out how it works, e.g. before the neutrino was discovered, beta decay defied conservation of both momentum and energy. But it would need radically new ideas to understand it which we don't have yet, I don't find Shawyer's explanations credible, I think few do, but the experimental data is intriguing enough so that it is absolutely necessary I think that someone follows it up just in case there is something to it, whatever it is (if we'd dismissed anomalous data we'd never have discovered the neutrino). See  Suggestion: The EM Drive Is Getting The Appropriate Level Of Attention From The Science Community

And also Mach effect thrusters: Woodward effect. Similarly very much a minority view but I'm glad someone is exploring the idea just in case.

Or spacewarp if that was possible from a planetary surface, and without damaging the planet in the process, which seems a bit unlikely?? Maybe if it can be very controlled somehow. Or teleportation as in Star Trek - turn something into information based on photons, beam that up and reconstitute that - but according to ideas at present anyway the amount of energy needed would be literally astronomical, and it involves basically destroying the object right down to its atoms and reconstructing it so you still need material in space to reconstruct it from.

Or the idea of portals, doors you just walk through and find yourself somewhere else. We don't have any ideas of experiments to do with that at present.

Those are all far future science fiction speculations at present.