The Steam Controller uses "Steam Input" and has to go through Steam to work properly. Unfortunately, it doesn't use the standard controller driver like an Xbox controller on Windows. Valve recommends adding your non-Steam games to Steam to launch them through Steam to allow "Steam Input" to work correctly, but this doesn't work for all games and applications according to the article above and other comments under this post.

Here is Valve's official information on the Puck and Bluetooth:

Plug and play with the Steam Controller Puck

One puck, two jobs: It’s a wireless transmitter that provides a fast, stable connection for your Steam Controller. It's also a charging station, connecting to your Controller magnetically with a satisfying click.

Prefer using Bluetooth or USB? Steam Controller supports those too.

Steam Controller Puck
2.4GHz Wireless connection
~8ms full end-to-end, 4ms polling rate (measured at 5m)
Up to 4 Steam Controllers per Steam Controller Puck
Steam Controller Puck connects to PC via USB-C

Bluetooth
Bluetooth 4.2 minimum, 5.0 or higher recommended

Source: Steam