Does the "brand" include the physical shape of the connector?
Could I make hardware with a "NotHDMI" port that "happens" to be mechanically compatible with HDMI plugs, has the exact same pinout, etc etc?
Even then: In the OP case the hardware is already there, it's only about the driver. So wouldn't a driver for hardware that very clearly identifies the port as "HDMI" run into the same problem, even if the driver itself never mentions the term?
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.
They are not quite the size of Valve though, and can expect people to figure out what that that port is.
> https://picockpit.com/raspberry-pi/raspberry-pi-pico-video-o... (scroll down to "DVI")
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).