@doctorowl For now, at least, Stadia requires a Chromecast Ultra device and does not support anything with embedded Chromecast functionality. This might change in the future but there aren't really any guarantees.
If you want to play on your TV, I'd recommend picking up a Chromecast Ultra - and, for now, the only way to get the Stadia Pro subscription needed for immediate access is as a part of the controller + Chromecast bundle anyway.
We don't know how far they'll take the casting functionality beyond the Chrome Cast Ultra. They may eventually expand it to tested devices but for now they are limiting I imagine to limit variables as they do wide audience testing.
You can however play on your phone or PC as well with traditional controllers and/or KB+M.