If each game is played to the end (no resignations, at least in the sample set) then presumably you could make good initial guesses about the victory condition by looking at common factors in the final positions. A bit like zendo. It wouldn't solve the problem, but it doesn't rely on optimal play, and would narrow the solution space quite a bit.

e.g. in the connect-four example, all final moves create a sequence of four or more in a row. Armed with that hypothesis, you look at the game tree, and note that all non-final moves don't. So you know (with reasonably high confidence) that making four in a row ends the game. How to figure out whether it wins the game or loses it is an exercise for the reader.

(mental note, try playing C4 with the win condition reversed and see if it makes for an interesting game.)