You could buy a game and play it on Stadia, you did not need a subscription. The subscription was to play the included games and get a few new ones each month.
The controller wasn't bizarre, it used Wifi to connect directly to the servers to reduce latency of it having to go to your device first via bluetooth then to the servers, hence why 'it didn't work with anything else', which is also not correct, it worked fine wired, you could also use an xbox controller just fine which is what I did, it wasn't something that 'shipped' with Stadia, it was an optional extra.