You can replicate mouse clicks with touch gestures on the screen, but those games that require a stick will need to have a physical command. You can also an android TV with Steam Link.You can connect your computer with ethernet for using Steam Link.

You can pair a Steam Controller to the smartphone thanks to the latest firmware update for the Valve controller, although you can use any other Bluetooth control system. The latest versions of the app will also allow you to connect remotely even if you are not on the same network, but the quality of the broadcast will be lower. It will be necessary to pair your device to the machine on which the Steam client will have to be installed and pair it so that what you will see on the screen will be nothing more than a mirroring of the PC screen, so you will need a WiFi connection quality and, if possible, have the PC connected to the wired network. It is a retransmission tool, so you will need a PC with the game running. Steam Link is the official Valve app for Android with which you can play your Steam video games directly from any Android device.

Steam link for windows