There are several developers working towards this right now! Unfortunately most of these projects are still in the "Crowdfunding" or "Pre-order" stages.
One promising board, the "UP-Board" currently on Pre-Order: http://www.up-board.org/
16GB EMMC memory
Intel processor (Compatible with Windows 8.1/10, Unknown if compatible with Linux)
You might be able to fit a low-profile nVidia GTX 1050 or 1050Ti in there, and that card would allow some modern gaming, but that is definitely not a gaming PC. The GT710 is an old business-class video card that is often used to allow multiple monitors on the same workstation, but is as bad as some on-die processor video adapters when it comes to processing....
You can buy used. For example, This - HP DC7800 Ultra Small Form Factor Desktop Computer (Refurbished) - is an extremely cheap x86 platform that does actually have some upgrade potential. It costs $50, but is more powerful than some SBC options and certainly more configurable.
It is the cheapest such machine I am aware of from large suppliers online. You ...