He hasn't said this. Just said that the institution of the Dalai Lama might not continue. And he hasn't said it won't either. He says that it is up to the Tibetan people to decide whether it should continue, and that based on this he will make the final decision later on.
In Buddhist teachings most people don't try to identify their previous lives. Buddha warned against it. Though he also talked about his own previous lives :).
For most people, to try to find your previous incarnation just leads to lots of confusion, suffering and misunderstanding, so he advised against this. But since he talks about his own previous lives, obviously it's not totally impossible for anyone to do this. If you accept that he could remember his own previous lives that is.
So - in most Buddhist traditions then you don't try to identify which people in this lifetime were also Buddhist teachers or respected for their understanding and insight in previous lives. As far as I know, it is only done in Tibetan Buddhism and related strands of Buddhism.
So if they stop identifying reincarnations of the Dalai Lama that would be nothing unusual at all. Doesn't say anything about what his future lives might or might not be, just means, stopped trying to identify them.
The thing is, the way it works at present, as I understand it, the process of identifying a new Dalai Lama involves co-operation between the Dalai Lama himself who leaves instructions about how to identify his successor, and those who follow those instructions. So if he doesn't do this, then that's the end of it, so he has to co-operate for it to happen.
With the modern reincarnations of great teachers in Tibet they don't claim to be able to remember their own previous lives as far as I know (again do correct me if wrong anyone) So not quite the same as the Buddha who said he could. The Dalai Lama doesn't tell stories of his previous lives through direct experience like the Buddha.
It's rather that they can to some extent direct their rebirth and leave signs to help find it - and that then the young child also has enough of a connection with the previous life that you can confirm this connection through tests, though they forget as they get older. Something like that.