You might instead be thinking of the Steam Link, which *was* produced by Valve, and *was* a tiny little brick that let you play games on your TV. But the Link wasn’t running the games itself, it was streaming them from a dedicated PC (which may itself have been a third-party Steam Machine) elsewhere in your home. https://en.wikipedia.org/wiki/Steam_Link
For Alienware (not sure about the others, but AW was Valve's lead partner on it anyway) you're right in that it was a computer designed by Alienware not Valve, however it was a) very different to other Alienware PCs, and b) Valve were genuinely part of the development process, they didn't just say "hey make a small computer". They also shipped with the first gen of Steam controllers, which were created by Valve themselves. (Unfortunately, due to delays with SteamOS, the first version of the AW "Steam Machine" actually launched running Windows only, but with the Steam Controller, because Alienware weren't willing to delay their launch further and instead developed their own controller-based UI for Windows in a rush job...)
(Source: me, I was in the loop on those goings on at the time.)
To this day, I think the Alienware Alpha (as the Windows version got called) was one of the nicest machines Dell ever made and one of the best small PCs I've ever seen.
The best goddamn controllers ever made, too, I still have one in a box somewhere around here and I won't use it because it's so awesome I don't want it to break. Pretty dumb eh? The two touchpads were the absolute best, I've never had control like that in an FPS and to this day I can't play any FPS with a stick because I was ruined on the Steam Controller.
I've never been a console/controller gamer, but I remember the first time I saw it - it was an early fake, that looked and felt very similar to the end product but inside it just had a metal weight and no actual electronics, and it seemed like such an exciting product, it was genuinely hard to keep that secret...
(And come to think of it, I think I misremembered when writing my last comment - I might be wrong, but I think the Alienware Alpha that launched with Windows actually shipped with an Xbox controller, and the steam controller was only available once the proper Steam Machine version was out. Not 100% sure, maybe we just needed the Xbox controllers for the press sessions before launch...)
It's the absolute worst controller I've ever used (Joy-Cons are a close second).
I didn't use it because I hated it so much, put it straight back in the box after a few days of trying to use it and eventually I sold it for as much as I paid, and I was glad to see the back of it.
The size/shape of the controller as a whole was fantastic but I just really hated only having touchpads instead of sticks, and that made it unusable.
Sticks work really well for me in terms of controllers, I just wish we weren't being shafted by stick drift all the time when manufacturers could be using hall-effect sticks; I've got 2 PS5 controllers and 3 PAIRS of Joy-Cons with drift, while I also have my original 2 x PS1 controllers from my childhood, neither of which has drift.
As someone who at the time was VERY into buying the “console-like” PC gaming experience that Valve was seemingly selling, I remember being pretty disappointed not just by the SteamOS delays, but also how much most of the Steam Machines still basically looked, to me as an uninformed buyer, at least, to basically just be a different SKU of their regular lines rather than the true “Steam experience” that I was hoping for (and which the Steam Deck eventually delivered).
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.
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 I've ever used. No frame drops or artifacting, even on scenes that make the 3090 chug. It forwards controllers to the PC.
Now, the software, "big picture mode" and otherwise using a controller for PC input aren't the greatest, but you gotta figure it's me and like 2 other people still using this.
BTW airscreen/miracaat/screen mirroring/"wireless display" all suck. If your TV has smart bullt in that supports miracast, that in my limited experience is the second lowest latency, then firetv devices, and then roku and everything else. Roku only usable for presentation or digital signage, unless first party built in.
No idea why.
Conclusion: it has been technically possible to cast to a tv for some years.
firestick was <100ms network and barely noticeable input latency (on the order of ~20ms so interframe lag at 60fps). steam link is link latency + some small constant - whatever the "frameserver" processing takes, call it 3ms but definitely <10ms - and that's both network and input.
when i said network i meant both the network and the actual refresh of the screen. watching a movie is one thing, but pushing "Y" and your character jumping should be "as instant as practicable" and steam link is the only one that is that that i've used, so far.
Unfortunately, while it was certainly a boom in the number of games Linux users could play (easily enough for me to ditch Windows entirely and game exclusively on Linux and consoles), it wasn't quite the critical mass needed for Steam Boxen to be a commercial success. Proton was the missing piece.
Had to find a friend with a Windows box to run a firmware update to make it entirely Bluetooth compatible. But it works.
First the steam box then the controller, I’m sure they learned a lot from both of those before they released the deck.
Maybe Valve has such excellent staff retention that this would be a non-issue. At my previous employers, two years would have been enough to have to start over from 0.