Most HDMI cables you'll use in a home theater or computer setup will just transfer audio and video, but there are ones that can also transmit Ethernet.
I have a PC based on an ASUS TUF 450 mb with a Radeon cpu. I run a cable off the mb HDMI output to a splitter, one cable going to a flat screen, the other to an Epson projector. Works fine, but the ...