I've found 3 "solutions".
None ideal.
Firstly, a device is required to convert Touchscreen information into useful, formatted info that can be sent to the Apple TV. This can be something like a Raspberry PI type of thing.
Then the Apple TV needs to receive it, and your app needs to find a way to interpret this as the input it's going to focus on.
With the obvious out of the way, the three ways to handle the touch info sending:
Bluetooth LE transmission and reception by the AppleTV. There's no CoreMIDI BtLE access on Apple TV, so must be custom, internal to the app. Paring, etc.
Ethernet, RJ-45... from one "server" to another... this kills the wireless connectivity of the AppleTV, with custom handling code that's then passing this into your app.
Wireless information sent in this server pretence manner, and then interpreted by the app. Probably the best of the 3 ways.