Seems like mobile gaming probably. Maybe something to plug your Google Pixel phone in and boost it similar to the Switch docking, so you can play mobiles on TV with the phone as a controller. Don't see them getting into games games, shit's not worth the money at this point.
There is a gaming revolution on the horizon. So much money in the industry and it's only going to grow. But I agree that Google shouldn't get into actual titled Games, they have the pockets to transform the industry, if they have the vision.
Esports is on the verge of exploding, but everything is still so young.
When you guys mention "Streaming" above, I'm not sure if you mean Twitch/Youtube streaming, or an actual game-streaming setup where you can finally disconnect people from hardware, and only require input devices.
For example, setup gaming servers like they do for Cloud computing, a gamer only needs KB/Mouse or Controller for inputs.. Connect ANYWHERE and let the off-site computers do the rest.
Gaming is so fragmented between consoles/mobile/PC... and the traditional PC is dying.
Once gaming is offloaded you open up a tremendous amount of possibilities:
1.) Cheating becomes near non-existent
2.) Streaming/Broadcasting changes dramatically. You now connect your Cloud Gaming account to your Twitch/Youtube, not relying on Streaming hardware of your own, also professional gaming broadcasting becomes more viable for public (non-LAN) tournaments.
3.) Latency is minimized, except between input device & server
4.) Might open up larger worlds, allowing more on-screen characters, VR, etc... Can optimize games to use the cloud computing/more powerful servers in ways yet imagined.
And this is just 1 aspect of the gaming revolution we've yet to experience.
Esports is on the verge... Another 10-20 years might see 1 of the big 4 (USA) sports (Baseball) take a backseat to video games.
Gaming arenas/stadiums
Gaming bars/clubs
etc.
1st step is it needs to be much more accessible.
FortNite has done this with their Every-Device approach.
It can be better.
Once gaming is accessible to everyone then you'll really start to see an explosion in the industry.