I agree... it is not spelled out very well in the regulations. The easiest way to look at it is, any fish that is listed in the creel and length limit guide is a game fish.
If it is NOT not listed here, it is a non-game fish.
HOWEVER, that rule still isn't 100% accurate.
Even though skipjack are listed, I'm pretty sure they are NOT game fish and you can spear them (although it's doubtful that you'll get the chance. They're fast!)
And another exception is catfish. In an effort to "upgrade their status" in anglers' eyes, wildlife regulators declared catfish a "game fish." However, they threw in the caveat that it IS still legal to shoot them (with bow & arrow or spear).
BUT, to be sure my assessment is correct I strongly urge you to call TWRA (1-800-262-6704) and ask.