The Rift exists in other games, even if it's not explicitly called out as such, simply by the fact that characters from those games can make cameos in other games. (Dissidia can be an argument that it exists in all games to some extent.)

FFV: Gilgamesh travels to all other worlds/games where he appears via the Rift. With the exception of FFXI, all Gilgameshes in other games are the same as this one.

FFXI: Shantotto is a canonical dimension hopper, but so are other shards/shades/versions of herself, which is what the whole "A Shantotto Ascension" mini storyline was about in XI.

FFXIII: Lightning can canonically hop dimensions.

FFXV: Noctis got pulled into the Rift by accident during his XIV crossover.

Presumably anyone from XVI who travels to XIV would also do so via the Rift.