How to get 1080p quality on my laptop?

[Klokhag]

I'm using a 1366 x 768 res Lenovo Thinkpad with a Mirabox capture card in attempts to record 1080p 60 from my Xbox One S.
I have so far only managed to get smooth footage at grainy 720p 30 ish. Is this because of my laptop's 1366 x 768 res, or the capture device (would Elgato yield better quality in comparison with Mirabox?), or can I somehow get smooth 1080p footage through OBS settings? See the second image for an example of the grainy 720p footage.

 

[TryHD]

I have so far only managed to get smooth footage at grainy 720p 30 ish. Is this because of my laptop's 1366 x 768 res

That has nothing todo with your laptops resolution, it actually doesn't matter at all in a capture card case you could even do 2160p with fast enough hardware and here is the problem. Your laptop is to slow for 1080p 60 FPS. On such a old plattform Quicksync is not fast enough for 1080p 60 FPS and CPU rendering with x264 you lack even more horsepower for it. So in conclusion, your plattform is not able to do 1080p 60 fps. Get a PC with a Nvidia 1650 super and you are fine.