My laptop is running the broadwell HD 5500 and have a decent game list of League of Legends, Factorio, Mini Metro, Portal 2, Mass Effect 2, Tomb Raider 2013, Civ 5, Besiege, StarCraft 2, Overwatch, and probably a few more.
Most of these games aren't too demanding so they run at around Medium or High while games like Tomb Raider run at a mix of low and med settings.
While HD 620 isn't a real leap in graphical performance, it should run a little better than what I have currently. So I would say it should modern games at maybe low settings.