While Microsoft and Google are getting ready to duke it out over their cloud gaming services, Valve still has a foot in the market. They might be throttling production of the handy Steam Link device, but the software lives on - and you can use that to stream games "from any computer running Steam".
A beta update to Steam Link rolled out earlier this morning, adding support for "Steam Link Anywhere". According to Valve, the update allows you to "stream games to your Steam Link from any computer running Steam, as long as your computer has good upload speed and your Steam Link device has a good network connection".
After you've downloaded the Steam Link app on your Android phone - Apple are still blocking it from sale - your phone will then search for a PC running Steam on the network. You'll be given a four digit code to pair the two devices, and Steam will then run a bandwidth test, starting at 5mbps and going all the way up to 100mbps.
I gave Evolution a quick test, which seemed like the best sort of game for touch controls. It was playable, although there was still a fraction of input lag. You can also connect a controller to your phone if you need more precise inputs for more demanding games - like a racer or Dark Souls or something.
You'll need to be in the beta branch of Steam to get the update, but you can find instructions on how to enable that here.