The reason why other games enter the story is:

“Mankind was tired of being alone with pets and other animals. For some reason, a mad scientist created the NinSegaEnixDraw Machine, which you could bring people and monsters for other games, created in 2047, 3 years before the Robot-Demon War. Some characters were:

Link, Zelda, Malon, Talon, Impa, Ganondorf, Samus Aran, Mario, Luigi, Peach, Daisy, Rosalina, Toad, Ash Ketchum, Squall, Rinoa, Zell, Seifer, Quistis, Selphie, Marine from DOOM, Jin Kazama, Jun Kazama, Kazuya Mishima, and lots of more.

Turns out, the monsters could come as well, and someone dumb did bring to our world only Final Fantasy monsters, some were freaking ugly, because of mods. That happened a day before the war.”

And there you go. Here is the reason. Everything belongs to their creators.