This would be possible. Bear in mind that the compute stick is a PC in a very small form factor, so the type of configuration that you are suggesting has to be done through some type of software that you need to install or by using a feature already present in the operating system, basically you are asking if you could use your laptop or Smartphone to control another computer.
You can try with Microsoft* Remote Desktop and also you can search for some Smartphone app to control a pc, there are plenty available online for you to try.
You can visit the following link to learn more about Microsoft* Remote Desktop Connection:
I feel that RDC is an overkill. I don't need to see the remote pc screen, I've got my TV screen for it. I tried to look for free PC or smartphone controlling apps, but couldn't find any that work without a hardware addon. Any ideas?
We can wait for other users to share their Ideas.