Ages ago I spun an aws instance w/ Grid, setup VPN and used Steam in-home streaming to accomplish a similar result. Using spot-instances resulted in something like $0.06/hr if memory serves (which it seldom does).
Biggest caveats at that time were setup time and latency; since I was too cheap to preserve the instance volume and too lazy to split the steam save folder to a smaller separate volume, and had yet to secure gigabit fiber.
It was more of a dalliance for me since I don't game often anymore, and if I'm honest with myself I enjoyed setting up the infrastructure more than I did playing Fallout 4. Please note this has more to do with how little fun I am in my old age than any problems with the game.
Although it seems likely this may raise more questions for you, or anyone, than it answers.
Edit: Like "Where did I put that Xbox controller..?"