I mean, have you seen "TF Card" slots?

You reminded me of the flipper zero video game module[0] with it's "video out port" which "transmits a video signal in DVI-D format to an external TV, monitor, or projector".

They are not quite the size of Valve though, and can expect people to figure out what that that port is.

0: https://docs.flipper.net/zero/video-game-module

No, the connectors wouldn't be regulated, you're not violating any IP by buying them and there's no prohibition on any of the manufacturers selling them to unlicensed companies. At worst you can assert a patent against the design but there's no specific patent for that design, there are patents for some aspects of the design/implementation but they're hold by the manufacturers of the connectors themselves.

There have been many examples in the past of consumer electronics companies selling things that are electrically and logically compatible with HDMI, but they just have to avoid using the word HDMI.

Probably one thing that the HDMI forum is holding over AMD/Valve is that there's an API to manage some of the functions of the HDMI driver. They could infer that this API is a part of the closed standards of HDMI Forum. But 90% of the threat is about certification and branding I am sure.

> Could I make hardware with a "NotHDMI" port that "happens" to be mechanically compatible with HDMI plugs, has the exact same pinout, etc etc?

Yes there are a bunch of products that do exactly this, sometimes with the same pin out and used for video output to HDMI compatible screens (internal HDMI mods for consoles are an example), other ones that use it for completely different purposes like controller ports (the Bliss-Box adapters and MiSTeR SNAC controllers). They just can’t use the HDMI name. In fact a few of those HDMI console mods started with HDMI in their product names and changes them for exactly that reason (e.g. DCHDMI now called DCDigital for the Sega Dreamcast).