I believe it's the repetition rule that makes the game finite, not the stalemate rule, since number of positions is finite.

There is also the 50-move rule of course which limits more drastically the length of a game.

Right, that would make more sense to me. Although it should be stressed that neither threefold repetition nor the 50-move rule work automatically. They need to be claimed by one of the players. If neither player does, the game can go on.

The 75-move rule does work automatically though, so the game is still finite.

Frankly, I wasn't aware of the 75-move rule! This indeed caps the length of possible games.

The threefold repetition rule doesn't have an equivalent (there's no, say, "fivefold repetition" draw that could be enforced despite the players' will), but it's really irrelevant from the perspective of solving chess, because there's no point in analyzing what happens if game goes through the same loop 1, 10 or 100 times.

And the 75-move rule sets a hard limit anyway, so you couldn't loop infinitely, even if it mattered.

> there's no, say, "fivefold repetition" draw that could be enforced despite the players' will

There is exactly such a rule. See the FIDE Laws of Chess [0], rule 9.6.1.

[0] https://handbook.fide.com/chapter/E012018

Lichess.org actually does have a 5fold repetition rule that applies without players claiming it -- https://lichess.org/faq#threefold

Kind of funny that your hypothetical example was exactly reality in this case.

I think this is what I was referring to.

OK, so that's not a stalemate. A stalemate is a situation in which one of the players has no legal moves (but isn't in check, which would be checkmate).

It's a typical mistake to equate chess draws with a stalemate, possibly due to the broader, idiomatic meaning of "stalemate" in common speech.