Not explicitly, but when you consider the "cannot repeat the same board layout three times" rule, the number of moves possible in a game does have a limit.
The 3 repetition draw rule has no bearing on the number of possible chess positions. And for the number of possible moves in a game the 50 moves with no capture or pawn move rule is a much more stringent limit.
BTW, the 3 repetition rule only comes into play is one of the players invokes it ... games can legally have more than 3 repetitions, but not more than 5 repetitions.
I didn't know it required a player to invoke it, I was basing the statement on chess implementations I've read (and written) where it kicks in automatically... but the 5-time limit you mention still supports my case that there's an upper limit. As long as the number of pieces remains the same, there are a finite number of arrangements for them so eventually (after a finite number of moves) a position would be repeated enough times. If a piece is captured (or converted) it resets this but still yields a finite number of new arrangements. Eventually you either cannot avoid the repetition, or a win condition is met, or a draw for insufficient material.
Compare this to, say, the L game, where the number of moves is unbounded.
Your "case" that there's a limit isn't in question ... as I said, the 50 move rule is a far more stringent limitation. And those 50 moves cannot include repetitions--they are captures and pawn moves, which are irreversible.
If you read my comment that you responded to carefully, you will find that it is precise and accurate--as I said, the repetition rule has no bearing on the number of positions.
