I remember being pissed at Sony for misusing the popular brand term on a one-shot gimmick that they had no intention of supporting, back when this appeared in 2004 (roughly).
(Random A/V equipment thing here) BUT ALSO IT PLAYS GAMES! is not new for Sony. They have made oodles of TVs with PlayStations in them, and some Nintendo consoles got in Sony TVs if I remember correctly. There are even some outlandish things, like a beefed-up MSX2 with extra RAM for video editing and titling use. In every single damn case they have dropped these like a hot potato. Why make more when you can just relentlessly cut production cost so you lose less on your console late in its lifespan than at launch?
The "all in one console" that will sell you games, music, and movies from the comfort of your armchair for use on your television was a dream at Sony since the early 1990s (an American named Mickey Schulhof was one of the proponents of the idea, and still is, though he was booted out of Sony partly in connection with the Sony Pictures "fiasco" - at least it was seen that way at the time) but it is only really becoming practical with the widespread adoption of broadband and hard drives in consoles. It simply would have been too expensive, even in the PS2 days (as the "PSX" demonstrates), to roll it out universally.
For a while Sony had a lot of us talking about PS, PS1, or "PSOne" games, which only pissed me off more. I'm back to saying PSX without a care.