A game having random mechanisms has absolutely nothing to do with whether it's deterministic.
Slay the spire is 100% deterministic, gameplay-wise. All the online poker games too.
There was even desync bugs even in live multiplayer games; there was detection that it desynced which would end the game, which in turn meant exploits that would intentionally cause a desync (which would typically involve cancelled zerg buildings for some reason).
This non-determinism would not and did not cause replays to diverge (the PRNG seed was most likely stored and would reproduce exactly the same results).