What is this approach called?

Cloud gaming is the approach described. The demanding game runs on a powerful computer in a distant data center, and only the resulting video is streamed to the player's screen, while button presses are sent back to the server controlling the game, meaning even an inexpensive laptop or phone that could never run the game locally can still play it smoothly.

Local rendering describes the traditional opposite approach, where the game actually runs on the device in front of the player, and split screen refers to dividing one screen between multiple local players, neither of which matches the remote-server streaming setup being described.

Because the round trip of a button press traveling to the server and video traveling back must happen in a fraction of a second to feel responsive, latency, not raw graphical power, is the biggest technical challenge determining whether a cloud gaming service feels smooth or laggy.