You can play two different games….unless one of those games is Dota 2

Overwatch isn't going to kill TF2. While, yeah, when Overwatch launches the amount of players playing TF2 will take a significant dip, unless Blizzard plans on regularly updating Overwatch with new content over the course of several years, the people will get bored of it and go back to TF2, as Valve is nowhere near done updating TF2.