You can have multiple systems (“households” in Sonos-speak) on the same subnet. When setting up the second household, if necessary having factory reset the relevant units, temporarily power off the first household and create a “new system”. You’d probably want to leave one set of controllers dedicated to one household, and another set for the other.

Note that you won’t be able to group speakers in one household with those in the other.

Separate “systems” would be a very frustrating user experience. In the SONOS world a “system” is installed in a home and there are separate “Rooms”. Rooms can individually play their own music or be “Grouped” (in any combination) to play the same music. In your case each TV would be a separate Room, each playing a game. For a party you would Group the Rooms to play the music. Only one network is required, wired or wireless.