But the basic assumption of standard game theory, which I presume he means to include in CDT, is that the agents can predict each other's behavior -- it is assumed that each will make the best move they possibly can.

Not quite. A unique Nash equilibrium is an un-exploitable strategy; you don't need to predict what the other agents will do, because the worst expected utility for you is if they also pick the equilibrium. If they depart, you can often profit.

Non-unique Nash equilibria (like the coordination game) are a classical game theory problem without a general solution.

Classical game theory uses the axiom of independence to avoid having to predict other agents in detail. The point of the advanced decision theories is that we can sometimes do better than that outcome if independence is in fact violated.