Oh gawd no, don't get a newer graphics card!

It would probably only make the problem worse!
What I meant was that Aspyr may have ported Life Stories at a time pre-dating your graphics card. The peculiar graphics artifacts reflect an incompatibility between the game's assumption of what card you have, and the graphics card drivers, which Apple has provided for your hardware. This can be solved either with a driver update, which would come from Apple under an incremental update to your OS, or a patch to the game by Aspyr.
It would help to know what graphics card you do have, as some issues were already addressed as I say, by Apple. If you know that you are already current on Mac OS updates, then I think you've done the right thing to open a ticket with Aspyr. A casual search at macgamefiles doesn't show any patches for that game.
If you like this game franchise though, I'd suggest getting the full game and any EP after maybe EP4. That combination isn't any more demanding, yet has better stability and support than the Stories knock-offs.