Being a media player was an integral part of Playstation since the PS2 era. The PS3 was essentially the thing that really pushed Blu-Ray over the line to really cement Blu-Ray as a movie format over HD-DVD.

Movie playback has been a thing for home consoles for decades. It became kind of a joke that the most played Xbox 360 game was Netflix. As more people have moved to streaming media/digital marketplaces, its only natural for those to grow. I've known lots of people who use their Xbox as their main media center that consume movies on Microsoft's storefront. It makes sense Sony would be in the game as well, as after all they even directly produce a lot of content themselves.