I'm slightly mistaken! There was a temporary 3-week event last November with a 4-player PvE story as Overwatch agents going on an actual mission. But other than that, gameplay has been all non-canon.
https://overwatch.gamepedia.com/Overwatch_Uprising
Should be another one this year, we'll see what they do with it.
Anyway, expanding on what I said in the previous comment, it's a neat narrative structure. Rather than "here's a game, go play the story" they've given us a game and then having released it are now telling more of the story out in bits and pieces. New map, new comic, new animated short, new character, new voice lines, anything like that related to the game is a chance to flesh out the world, its history, and where the conflict between Overwatch and Talon is headed.
I think my favorite part of it is the environmental storytelling. Every level has some significance to one or more of the characters (video from the previous comment takes place at Eichenvalde), and there are bits and pieces of lore scattered throughout. The name that we see being carved into the bar at the beginning of the video exists in-game at the start of the level (and has been there since launch). In the present-day, with the non-flashback portion of the short having now taken place, the Overwatch emblem that Reinhardt sets on the armrest now exists in-game at the same location.
On another level (Ecopoint Antarctica), you can see the cryo-chamber where all of Mei's colleagues went to sleep in the pods to wait out a storm, and then never woke up. There's an animated short telling that story as well.
What's remarkable about the game is how well it functions as "just an action game" with bright colors, fun characters, really great gameplay, and gorgeous level design. But if you want to look into it deeper, there's a pretty big world with some heavy stuff going on.
I'm going a bit fanboy here, but if you're into shooters definitely check this one out.