I'm wondering if we should come up with better name for this kind of signal transfer, and for "HDMI over CAT5" as well.

This system gets an HDMI signal from one place to another, but not via an HDMI cable. Similarly, RF remote control systems get IR from one place to another without wires or light, but we don't call them "Wireless IR" or "Lightless IR," we call them RF systems. We don't call voice radio transmissions "sound without air," either.

Sure, this wiring HDMI system has an HDMI connector at each end, and it meets HDMI specs for video, handshake, etc, but there is no HDMI signal on the RG6. Voice radio communication uses a microphone at one end and a speaker at the other, a case parallel to this one, but it's called radio. And HDMI is a wired connection using HDMI cables with many conductors, HDMI connectors, etc.

If we continue to call this HDMI over RG6, there's no logical reason not to say that some particular piece of RG6 is an HDMI cable. It's carrying an HDMI signal, right?