I would say that the introduction of streaming gameplay on platforms like twitch and the pro-gaming scenes build up is one of the largest shifts. Making gaming not only interactive form of entertainment but also for spectating. Everyone can choose to be the little brother who got the unplugged controller and had no real impact of what happened on screen.
I'd say another related but distinct change is the release of the first moba-genre games. Competetive, temwork but still with individuality through the characters.
The larger shift of multiplayer from couch or lan to online is probably my vote for the most impactful change to gaming. Sure it started in the nineties but it the perfection of the formula happened later.