There's no need for the wall to actually be infinite in the implementation itself. Games are 99% smoke and mirrors. The game could easily be despawning bits of wall that are too far away and recreating them on demand.
Doing so with the right algorithmic approach would make the wall generation "stable" (that is, if you fall enough and then climb back up, it'll be the same wall layout and not a new random layout). There would be some kind of limit to that based purely on the limits of integer sizes, but this limit can be large enough that it is effectively infinite in practice. If the world eventually wraps (no idea if it does) you can even avoid ever showing the player any "edge" to the world.
The game also possibly moves the wall rather than the player. If the player moved, then eventually the player would move to some coordinate where floating point inaccuracies and imprecision would cause severe errors. Keeping the player at position 0,0,0 and them moving the wall avoids that, as the walls are despawned from memory before they get too far away from the origin.