It depends what rules you're using, but there are the three-fold repetition and 50-move rules which allow a player to force the game to end in a draw. The catch is they both require one of the players to claim a draw under the rule, otherwise they can keep playing.

There is additionally the 75-move rule where the the game is forced to be over without either player claiming the rule (the arbiter just ends the game), that rule would give an upper bound regardless of the players knowledge of the rules.

As I understand it, the 50-move rule must be invoked by one of the players, lets assume our immortal players agree not to invoke that rule.

The 75-move rule is automatic, so that would be the limiting factor.

Note, that 75-move rule is only applicable after no pawn has moved or a piece has been captured. So our immortals can do a lot of shuffling things around.

I'm thinking that the number of moves of the longest game is going to be (16 pawns * 7 moves each + 16 pawns being captured + 14 other pieces each being captured, not the kings) * 75 moves for shuffling around = 10650 moves.

That's only 1 week at 1 move per minute! But given the permutations, it might take much longer to calculate the actual moves required to get to the end state :)

In this lovely paper: https://tom7.org/chess/longest.pdf

The author points out that:

"This rule only applied to games started after its introduction, so it is possible that some pre-1561 games are still in progress and may never end."

How I'd put it is that there are two sets of stopping points under FIDE rules:

- After threefold repetition or 50 moves, either player may claim a draw.

- After fivefold repetition or 75 moves, the game is automatically drawn.

Most modern counts of the longest possible chess game, or the total number of possible chess games, are based on fivefold repetition and the 75-move rule.

Meanwhile, threefold repetition and the 50-move rule are still relevant in endgame tablebases, since they rule out certain forced mate sequences.