The one you linked looks similar, but is off brand. The one i have has the only difference of a breakaway cable....so if you pull hard enough the cable separates instead of breaking your USB port.
Like
this but it is built in to the controller cord of the one i have. Not sure if you can even buy these anymore as i have had been using this since the xbox 360 has been the newest console.
The xbox one controller also has a USB charging cable. I havent used it yet for computer use, but i would assume that you could just use that to connect the controller to sync it.
You can use any USB controller. But i have found over the years the off brand ones suck and break easily or have driver issues in the future. Its best to just get a name brand one as you only have to buy it once and your done.
This is mine except black. If i needed a second controller, or broke mine... This would be the one i would order as it is 1) name brand and 2) listed as never used (new). I would not buy an off brandm as i have done that before and ended up buying numerous ones every year to replace them. Ive owned this one for probably ~10 years and it has endured drops, pulls, spills, and works as if it is brand new.
https://www.ebay.com/itm/Microsoft-Xbox-...0005.m1851