Yep, it would be very large if you stored the entire game tree. But as I understand it, using a neural net in the right way, you don't have to any more, the same way that AlphaZero doesn't have to store the entire astronomically large game tree for Chess. Instead you rely on the neural net to learn and generalize across states.

Doing this in imperfect information games like Poker in a theoretically sound way (i.e. one that would converge to a true equilibrium in the limit of infinite model capacity and training time) obviously requires a lot more care, and plus you presumably also get the other practical challenges of neural function approximation - e.g. having to make sure it explores widely enough, doesn't overfit, etc. But it's still good enough apparently to be superhuman, and apparently if done right you can throw away practically all abstractions and just let the neural net learn on its own how to generalize between between all those states.