Shield Controller operation

I'm finding that most games just work, and controller inputs go through without a hitch, but some games like Hollow Knight don't.

It's been driving me crazy the last few days thinking about how this all actually works.

For shits and giggles, I started Gamestream and went to the PC looking for an entry in Game Controllers, expecting to see some kind of virtualized Xbox controller listed, but the screen comes up empty.

So with no controller detected, I can understand why Hollow Knight wouldn't work.

And in another test, I ran Tales of Berseria, which under Controllers, actually detects a SHIELD device as its controller.

In a third test, I actually powered on the local XB1 controller connected to my PC, and then tried using the Shield controller from the ShieldTV and that doesn't work either, so it's not simply sending XInput commands through.

So how come the vast majority of controller-enabled games do work and there's those that don't? I've tried looking up how controller support for in-home streaming functions but results just show me how to connect Bluetooth devices.

Anyone have any insight on this?