At the very least, you really DON'T need to touch it, like you said! There is a card tournament, but it's not hard to beat with basic cards or anything you would pick up naturally anyway.Replaying FF9, and Tetra Master still is my least favorite mini-game / card game ever. It's just not fun and there is little reason to touch it. They should've stuck with Triple Triad IMO.
Triple Triad was fun, but it was also intrinsically linked to many gameplay mechanics, so it was both satisfying to play, and benefited you in the long run.
Tetra Master has only one small section where it benefits you at all, and the rest of the time is purely optional. And doing well in Tetra Master is way more complicated due to the way it's math works, to the point where it's much harder to get invested in it.
I wish Tetra Master was a bit easier to "get," it would be a ton of fun if it was. It's more of a collectibles game then anything as it is, though it can be fun if you do your best to understand the mechanics and get some good cards.
Triple Triad also kinda cheats, because success in normal play can be intrinsically linked to using over powered cards early like Ifrit and Diablos, so you can win when you aren't really supposed to. Tetra Master is on a curve the whole time, so you don't really get that taste of power Until you get far enough to earn it.