Yeah, I realize that and that’s a nuisance for a videogame… If the game is small enough, OP might be able to give it a virtual GPU with VirtualBox, I did it in the past to play with friends on a single computer. I don’t know if the usual KVM-based VMs support it as well.
If you don’t want proprietary drivers the choice is quite straightforward: AMD. The official drivers are open source.
As for my experience, I’ve had absolutely no problems in the last few years with AMD, but I have to admit that I have always been using an iGPU, which has always been good enough for my needs.
I used to have problems with Nvidia proprietary drivers, but that was at least a couple years ago, things might have changed. I’ve never had issues with the free unofficial drivers, besides worse performance.