Hey Zack,
I'm actually currently working on a research project exploring the challenges of licensing digital games in libraries (both on consoles and PC games from platforms like Steam). The long and short of it is that nobody is really licensing digital games at scale right now. Game publishers don't have models for licensing to libraries and other educational institutions, and there aren't library vendors for digital games like there are for ebooks and streaming video.
Right now, the libraries that are providing some access to digital games are doing so in the way that you're thinking about: having games preloaded on library owned machines. This sits in kind of a legal grey area because the digital games sold from console stores and online platforms are intended for single users, but no libraries (to my knowledge) have gotten in trouble with game companies for providing access to digital games in this way. I'm hoping to work on models for providing online access to digital games in ways comparable to ebooks, but we're at the very early stages of figuring this out in the library world.
So far, I've been talking with academic libraries interested in digital game collecting, but I'd love to hear from others in public libraries that are trying to start figuring this out, too.
Colin