> Is there any tech in the controller?
Yes. The controller connects directly to your game instance over WiFi. It doesn't need to go through a box first and be relayed (this can shave a significant amount of latency off controller inputs).
> What "costs" $129 if there's a subscription model attached to this?
For $129 you get a controller ($69), a Chromecast Ultra ($60), 3 months of Stadia Pro ($30), the full Destiny 2 game with all the DLC ($?? I forget).
You may be confused with how Stadia Pro works. It's just like PS Plus, you occasionally get a free game or two and it enables you to play at 4K in 5.1 surround sound. Without Stadia Pro you can still play any Stadia game you own, without a fee.
> why wouldn't there be compatibility with Xbox or PS4 controllers?
But there is compatibility with XBox and PS4 controllers. It was in the video and in their original announcement. You just can't really use them with the Chromecast AFAIK but you can with any computer and some tablets / phones.
> but why try and reinvent the wheel with a new controller?
You can bring your own or use theirs for the best latency / game experience possible on Stadia.