Are unique condition cards unique on a per-game basis, or on a per-player basis? I.e. if there is a RAC w/ Kylo Ren mirror match, does one player using the Kylo Ren action overwrite the ISYTPOTDS condion that their opponent placed on them earlier?

uniques are per player, and always have been. Conditions are no different. Dupes of a unique can exist if its between the players and not on the same side.

Uniques have always been per side; no reason to think that should change now.