There's a difference between consoles that were made as pure gaming consoles with multimedia functions, & consoles that were made as multimedia devices that also plays games.
Original Xbox, Xbox 360, Wii U, & PS4 are the former. PS3 & Xbox One are the latter.
A lot of this is simply marketing/advertising. Sony cares about it just as much as MS -- they simply had different plans. Sony took the (in my opinion) smarter plan in focusing on gamers first since hardcore gamers buy consoles early.
The PS4 is pretty much the only current Sony product that's doing very well. Sony has multiple services like Playstation Vue and their new deal with Spotify. They are using the Playstation brand to label their media services. Sony has many studios that make media. Yet you want to tell me the PS4 wasn't made to push multimedia? Can't say I agree at all.
The Wii U's gamepad was made with media in mind -- that was the way they advertised off TV play; Being able to play games while you or someone else watch sports on the big TV. This is on top of the TV remote functions and all of the (pretty standard) media apps.
The PS3 was as much of a gaming console as its predecessors. PS2's DVD push was similar to the Blu-Ray push of the PS3 -- both were the cheapest players of those formats during the time of their release.
The modern console isn't a straight up gaming box anymore. They are all multimedia boxes. The difference simply comes in how the features are advertised to potential consumers.
