Console-specific life:
Advances in short-range wireless connectivity will result in all devices using open protocols to communicate with each other with virtually no latency over farther distances than currently common. So if one wants to play their console on their screen of choice, no matter where the console is in their house, they just pick up their controller, hit the button, and the console streams it all with near zero latency (including for the controller) to their chosen screen.
Standalone VR headsets like the Quest 2 will by then be so powerful that their internals rival standalone consoles, and will play to any screen in either VR or standard formats, so some people take to treating their VR headset as their console.
General gaming:
Advances in networking technologies should make concepts like bandwidth and data usage archaic terms by then, because it should all be figuratively limitless for what an individual uses the internet for at that point (we're talking about 20 years in the future here). So cloud gaming will be the most common way to play games either at home or on the move. Cloud gaming services will compete for their own content the way streaming media services like Amazon and Netflix currently compete with on another now.
Mobile:
Phones will be almost as powerful as a dedicated console. Device screens will be easily made expandable and retractable at will which does away with the need for tablets - since everything is effectively a tablet.
The big rage for mobile gamers are a plethora of MMO's that take place in the real world thanks to augmented reality. "Our World of Warcraft" sells over 500m units in its worldwide launch week and has both new users for which WoW is merely an artifact of pop culture history, as well as now elderly veterans of the defunct WoW, buying it and seen wandering around city streets the world over battling virtual monsters together.