At the moment the best format to send video (and audio and control and power) over ethernet cables (5e or 6a) is HDBaseT but as Antoine pointed out you still need a transmitter (and a receiver unless your projector natively supports HDBaseT). More and more projectors support HDBaseT. Some use different names such as the Panasonic PJLink but it'll all compatible.
I wouldn't be surprised if HDBaseT outputs started showing up on computers (or HDBaseT GPUs) in the very near future but I don't know that there are any out there yet
I regularly send HD (1920x1080) over 200' of CAT6a cable with no degradation or latency. But keep in mind that HDBaseT protocol is different from TCP/IP protocol so you'd need to run a secondary ethernet cable.
Comments
For now, it looks like you'll need a video to RJ45 converter to send the signal over ethernet. Or try TCPSyphon.