Earlier quoted context omitted.
I suppose the missing part of the story is why they held back on pursuing this market. At the time, the console market was wide open, with little innovation in terms of hardware, until Nintendo released the Switch. Even now, I'd be quite happy to own a Valve branded, small form PC that plugs into a TV. The Steam Link was a kop out to me.
I still use my steam link all the time. I have it fiber back hauled to the computer that it runs off of. I'm thinking of buying a couple more. Give one to my kid and one put on a projector so I don't have to keep moving it back and forth. Also, I think the device you're looking for is a deck because you can plug that into a television and use a wireless remote with it. The steam link is the best remote display device…
Conclusion: it has been technically possible to cast to a tv for some years.