Android Mirroring with Scrcpy + Hardware Controller
In case you don't have an Android hdmi box but just a phone, this is the best way to play games on a big screen.
You can mirror your Phone to PC with the tool scrcpy, i'm using an usb-c cable by setting the bit-rate of scrcpy at 50M.
To play multi touch games with an hardware controller you can use the droidmoteIME functionality of the DroidMote Client.
DroidMote Client and DroidMote Server are running on the phone and with droidmoteIME enabled. DroidMote Client is connected to the local DroidMote Server.