XBOX 360 wireless controller & Android tv BOX

No, the 360 controller uses a proprietary wireless protocol

Xbox 360 controllers don't use Bluetooth, they have their own wireless protocol that Android phones can not use. The only way to use a 360 controller on an Android phone would be via a USB cable.

Hi MyNameIsMatt! My name is Ricardo an independent advisor ready to help you with this situation!

Of what you are using is a wireless display app, you won't be able to control the Xbox trough the tv, if your Tv supports android apps you should install the Xbox app, this will allow you to play remotely or while using wireless display the controller must be connected to the Xbox not the TV

Hi,

Unlike the Xbox One controller which can be both wireless and wired, the wireless 360 controller only operates via wireless. The connector for the USB - or the 'Play and charge' - cable only sends power, not controller input data. Also the wireless protocol
it uses is proprietary, in other words, it's not Bluetooth.

You can use an wireless 360 controller on a PC, but you'll need an Xbox 360 wireless gaming receiver attached to your PC.

The wireless 360 controllers do not work with Android, but the wired ones do.

Hope that helps.

Building a Steam box IS sticking with PC. It just means building a PC designed to work with a TV. Windows and a wireless keyboard and a 360 controller fit the bill.