Just as HDBaseT is not HDMI, HDBaseT is not ethernet.
HDBaseT uses technology similar to 10GBaseT, like 16 level pulse amplitude modulation, four twisted pairs, etc., but it is not compatible with 10GBaseT ethernet. For one thing, it is not packet based. As I understand it, among other things, the encoding scheme has been modified to provide superior forward error correction because, unlike ethernet, a bad packet cannot just be resent. Video data is being transmitted line by line in real time, and by the time a resent packet could be received, it would be too late to use it. My guess is that HDBaseT also doesn't use the four pairs the same as ethernet. For 100 Mbps etherent, that would require that two of the pairs be dedicated to the 100BaseT link, leaving only two pairs for the much more bandwidth intensive HDMI signal.
Valens originated what is now referred to as HDBaseT as 5Play. The idea was to be able to send video, audio, network data, control signals, and power over a single cable. HDBaseT essentially multiplexes all of these onto a single cable in a proprietary manner.