No, that how google was able to achieve better latency and allowed using it on Chromecast devices. The controller has Bluetooth used only for setting it up, from there it's Wi-Fi that used to send input directly to the cloud instead of "BT to showing the stream and then to the cloud".

I wish they enable Bluetooth for it because it's an excellent controller. I use it to play Halo on xCloud via iPad...

A friend gave me a Amazon Luna controller he didn't want.

I was pleasantly surprised that the controller synced via BT. I was able to play non-Luna FireTV games with no problems.

It even worked without the Luna software installed on my FireTV Stick (I don't recommend you buy a FireTV stick, nor any FireTV product really).

The concept of the Luna software is interesting: Cloud streamed HD gaming on low-end hardware. Game play was really responsive. Very little video artifacts. But like all other FireTV products, the UX was geared towards sales, not user ergonomics.

I plan to uninstall the Luna app and just play the few FireTV games that I have. Sadly Alto's Adventure is too resource intense for my FireTV Stick.

They have bluetooth and wi-fi hardware but currently locked and can't be used outside of Stadia. Wired USB works as a normal controller though.

They're WiFi, I believe.

Wifi