I'm not sure how quickly streaming will be able to outpace local twitchy gaming, but for online games streaming makes perfect sense.
The way online games work right now is your controller sends info to your local machine, and your local machine makes it "look" like you did something. But nothing really happens until the local machine makes a request to the game server sitting in a data center somewhere. So the latency between your action being processed and making it to the game server is:
Latency_input_client + Latency_client_server = Total_action_latency
So in the case of streamed games, this total number doesn't change. Its just that the client is colocated with the server now. So the latency between your controller and your machine is greater, but now the latency between the client running the game and the server is basically nothing.
The problem for the consumer now is that when they were on a relatively high latency connection, and all their actions achieved the desired result when they hit the game server, the video response lag time will appear significantly higher because it has to completely round trip to the server. Before the client can sort of "pretend" that your command is accepted locally, to make it look like you have faster response time than you really do. This is why when you are on a high latency connection you can end up with really jerky movements in some games, or sometimes an action you take gets rolled back. i.e. you thought you shot enemy but turns out they shot you instead.
So in general, I think for really twitchy single player games like Hollow Knight, local is still going to be the way to go because of video lag. But if you are playing Assassins creed multiplayer, which is a bit slower moving of a game and online, it probably won't make a big difference.