The HDMI Forum, responsible for the HDMI specification, continues to stonewall open source. Valve’s Steam Machine theoretically supports HDMI 2.1, but the mini-PC is software-limited to HDMI 2.0. As a result, more than 60 frames per second at 4K resolution are only possible with limitations.
I have actually been looking at modding an NES with HDMI (and other goodies) as a small project. There are various kits out there.