This app was mentioned in 10 comments, with an average of 1.40 upvotes
It looks like you can do something similar with this app over Bluetooth or WiFi.
^(Note that I just found this randomly on the internet and have no idea how well it works.)
AutoHotkey joystick control: https://www.autohotkey.com/docs/KeyList.htm#Joystick
You can also use a VPN plus a program like this on Android: https://play.google.com/store/apps/details?id=com.negusoft.ugamepad (note: just a random one I googled, not necessarily recommending)
Do you have a smartphone? You could use an app that acts as a bluetooth / wifi gamepad.
I don't think this is possible over bluetooth (at least not without rooting the phone) but there are apps that lets you use your phone as a controller over Wifi (with a program running on the host). At least on Android.
They're all absolutely terrible though, even for simple games. Looking at a TV/Screen while using a separate touch screen as a controller just feels bad and you end up missing the buttons on touch screen. It's just flawed as a concept.
Some ideas:
Have it show a random cat or dog doing cute stuff gif.
"Something to cheer you up today..." /r/UpliftingNews might have some good stuff.
If you add a microphone you can then let them use voice to do tasks like switch what is displayed on screen. Give them a tutorial while they poo. When they're washing their hands (hopefully they wash their hands) they can then repeat those words to the mirror.
"Tomorrow's weather, please?"
Then change it to something else and repeat it to them.
"Did you say... Play more dog videos? OK."
You could call that "Party mode"
You can have Sudoku - using coordinates if they play by voice.
Chess - same as above.
Use their phones as remote to play games... (I see there's an android app called "Ultimate Gamepad" - I have never used it so don't know anything about it.)
Anyway - just some thoughts.
(Edit: Corrections and clarifications)
I would like to add, there was no PC required (Some very similar apps, do the same, but require a PC as a host to connect the devices) The app i am referring too, i could use on a Train while travailing from one end of the country to the other. Like this: https://play.google.com/store/apps/details?id=com.negusoft.ugamepad&hl=en_GB
It should be possible. Download this app and use the control mapping function on the gpd xd. https://play.google.com/store/apps/details?id=com.negusoft.ugamepad&hl=en
https://play.google.com/store/apps/details?id=com.negusoft.ugamepad&hl=en
As long as your PC has wifi/bt.
Showed up after a simple google search "use phone as controller for pc"
Search Google play store for "soft controller" "touchscreen controller" or the like
https://play.google.com/store/apps/details?id=com.negusoft.ugamepad