Zermatt is better known, trails starting up above Zermatt with view of the Matterhorn and then descending all the way to Visp before using the train to get back up. I’ve no doubt you can study the maps and ride some trails to link up with the mountain railways and lift systems. The “Switzerland Mobility” website and phone/tablet apps are excellent and you have free access to detailed map and can toggle walking paths/mtb route overlays. The resort website lists the typical official Swiss MTB routes which are mostly fireroads !
As for road riding my recollection is that there is a single drag up from the valley / VISP and not many options for loops.
The Swiss segment of Strength in Numbers featured some trails around Zermatt but I think they cheated and had a helicopter ! Trails are a mix of Verbier and Zermatt.
[video]https://www.youtube.com/watch?v=ibsuJFlXqiw[/video]