dude, can you look up your tv/monitor? it's build and year, brand and stuff? a lot of display units have heinous lag (mine has one) so you can google stuff up or post the details of your tv here. with that said, windows pc does get paired with xbox one but the issue is this...
first of all, your console will send the information to the display unit via tha cable, which takes time since hdmi is digital and not analog like vgas used to be,
secondly, windows will process the data from xbox which will add precious microseconds to the response time, thus making it crappier.
In case you're playing a multiplayer game, the output will also be subject to ping and the strength of your connection. so think of microsoft's pairing feature as an addon but don't use it too much. lemme know if i'm missing something.
Cheers