Question

Is this game somehow Multiplayer?

The PSx version is single-player only. (Unless you consider sharing a file with a friend "multiplayer".)

If memory serves, there is a FFT for the Game Boy Advance. I don't have a GBA, but you might want to look into potential multiplayer options there. Chances are it's single-player on that platform, too, though.

I'm disappointed too. :(

Tactics advance has multiplayer missions, but they aren't very fun. The PSX Tactics, unfortunately, has no multiplayer feature. If you are looking for a tactics game that has a multiplayer feature, then I suggest Tactics Ogre, by enix for PSX.

You could always play FFT as if it was multiplayer by assigning a character to a friend, and that way between turns, you can just chill and have fun with friends.