Does it have to be "taking over"? Or does it only have to be fun? I suppose that Overwatch is 'taking over' on the competitive scene, or perhaps specifically in South Korea. But when it comes to just having fun it may or may not be a "main game" for many. Some just don't like Overwatch at all, or they liked it at first then stopped eventually. There's plenty of people playing Heroes of the Storm, or Smite, or Paragon, or when it comes to MMORPGs there's the obvious Black Desert going on right now.
Before Overwatch came out I used to play Mass Effect 3's multiplayer pretty much every day for about 3 years non-stop. Then sure Overwatch came out, it was new and refreshing, played it a lot like a lot of people did. Then I stopped with Overwatch for a time and went back to some Diablo 3, then gave a try to Elder Scrolls Online recently. I still play some Overwatch from time to time, but I think it's getting worse and worse as the months and new patches and "balance changes" come. I actually almost uninstalled it no longer than about two weeks ago, but I decided against it only because I want to at least give a try to the next hero when she comes out... then I'll see.
Mass Effect Andromeda is right around the corner, and it looks like they haven't changed the multiplayer formula too much from ME3, which is awesome for me. So even if the campaign sucks I'll probably play the multiplayer like there's no tomorrow for a couple of years. But I always end up playing something else anyway at some point. When I have a "main" game it never lasts more than about two months, because if I keep playing JUST one particular game non-stop then it always burns me at some point no matter if it's a masterpiece or not. I have to go look elsewhere from time to time.
So I dunno... suggestions for "main" games don't quite come to mind, but some online games I know that a lot of people play on a regular basis despite other big name games "taking over" would be:
- Heroes of the Storm
- DOTA 2
- Paragon
- Smite
- Black Desert Online
- Elder Scrolls Online
- Team Fortress 2
- Warframe
- EVE Online
- For Honor
- World of WarCraft
- League of Legends
- StarCraft 2
- Battlefield 1
- Diablo 3
- World of Tanks
- Grand Theft Auto V
- Guild Wars 2
- Rift
And well that's about what I can think of for now but there's obviously many, many more. For upcoming games... I for one know I'll be very interested by Andromeda's multiplayer but it's focused on 4 players cooperation, so it's not everyone's cup of tea. For other games... not sure, if you like fighting games you could always give a try to Killer Instinct, Street Fighter V, Guilty Gear Xrd or wait for Injustice 2 if you like superhero stuff, or go with Mortal Kombat X. The gist is that you'll probably have to give a try to most of the ones you think might interest you before you find your "main" game. That, or watch a lot of "Let's Plays", Streams on Twitch and gameplay videos on YouTube, etc (to make up your mind about one of them and then stick to it if it's your goal).