None of the presented solutions cover the aspect of being in a different place than the rack, the same network is fine, but at a minimum a different room.
If someone can show me a multi seat gaming server that has native remote performance (as in you drag windows around in 144 fps, not the standard artifacty high latency behavior of vnc) I'll eat a shoe.
Thin clients absolutely can do this already. There are a variety of ways to transmit low latency video around a home from HDBaseT solutions to multicast / network driven ones. Nevermind basic solutions like sunshine /moonlight... Nvidia variants etc.
I have a single racked PC for feeding my home which has 3 'desk' endpoints and two tvs... all of which are fed from the same location and can be dynamically matrixed (albeit the choke point is usb2 to each location because I'm cheap.). Latency is maybe 1.5-3 frames from live. Other solutions are normally around 5-8 which while higher are sufficiently snappy and won't effect competitive play (professional level notwithstanding.)
A lot of latency comes down to tuning your solution and research. The vnc method you refer to is the lowest common denominator running on ancient technology and codecs simply because it is a widely supported standard.
Edit: As far as 144 goes- I don't have any displays that run that but I have two running at 120 with no issue.