Gaussian splats don't offer the flexibility required for your typical videogame. Since it isn't true PBR its lighting is kind of hardcoded. Rigging doesn't work well with it. And editing would be very hard.
It's good for visualizing something by itself, but not for building a scene out of it.
Some intrepid souls are trying to tackle the global illumination problem! https://arxiv.org/abs/2410.02619
Wow!
Also, since it's slightly hidden in a comment underneath the abstract and easy to miss, here's the link to the paper's project page: https://stopaimme.github.io/GI-GS-site/
Early 3D engines and of course all the 16 bit 2D games had “canned animation”. Half Life was an early example I can think of that used real IK rigging. Unreal 1 did not.
People are working on recovering PBR properties, rigging, and editing. I think those are all solveable over time. I wouldn't start a big project with it today, but maybe in a couple years.
If you want a real cursed problem for Gaussian splats though: global illumination. People have decomposed splat models into separate global and PBR colors, but I have no clue how you'd figure out where that global illumination came from, let alone recompute it for a new lighting situation.