Even if I'm wrong, there's not much harm that could come from delaying our stat increase. There's very little risk and a potentially great (or at least decent) reward.
We should have 40+ skill points by the end of the game. +1 damage could save our lives, and we'll probably want to pick up +5 STR and +10 STR eventually, anyway, assuming we continue to use any physical attacks at all. Also, your "great reward" would probably be the ability to take +1 MAG right away, which we would be able to do the next time we levelled up.
We could be a Gish or an Artificer or something.
I don't know what a Gish is, so it's either A) in a weird blindspot for me, or B) obscure enough that it's probably not happening—and my inability to find it via a quick Google search suggests the latter. And while we
could be an artificer, I'm still not sure why the stuff we do is going to be magical. Unless I missed it, nothing relating to the book or machine has even
implied magic.
How do we know that we're using the FE system?
Well, we're pretty clearly using a weaponless version of the FE system for combat. Levelling is based wholly on the FE system, too, right down to the set of percentage-based growths.
In FE, does STR determine magical power as well?
No, that's MAG.