You just take the next train to Visp once you have gotten your luggage. You do not need to worry about particular train services. Trains are mass transit, and as such you do not buy a ticket for IC 820. You buy a ticket “Zurich Airport” to Zermatt. And that ticket allows you to take any trains on the route. And if you miss a connection, you take the next one. Now those 7 minutes in Visp are normally enough. A normal adult could make the change in 2 minutes.
Trains run every half hour on Visp - Zermatt, so nothing to worry about there.
Note that the cheapest ticket for your route is the Saver Day Pass. You should buy that ASAP. In fact, you should have bought that the moment you booked your flights, as these tickets are cheaper the earlier you book them.