pete_101 :
With the exception of a proper gaming laptop, most laptops just aren't powerful enough to run much more than browser games.
That's not entirely true. : P
I've used a laptop with an i5-5250U CPU and Intel HD 6000 series graphics for some light gaming, and it can maintain playable framerates at 720p at reduced settings in many games, particular those that are at least a few years old. It offers more performance than last-gen consoles (PS3 or 360), so a "non-gaming" system like that is certainly capable of more than just browser games, even if it probably won't fare well with most big games from the last couple years.
That being said, Intel's HD 6000 IGP is more than twice as fast as HD 3000, so that's likely to be more limiting. It's also pretty difficult to say how performance might be for a particular game without knowing exactly what that game is. Many games will recommend the hardware necessary to run their game at 1080p with high settings, but if you're willing to work with lower resolutions, framerates and graphics options, then lower-spec hardware might potentially work.
Doing a quick search for those requirements though, it looks like you might be hoping to run The Witcher 3, in which case I'd say it's not likely to work. With the in-game graphics options turned down all the way, and at the lowest resolution, you would probably still be looking at framerates below 10fps, which would be unplayable. That's one of the more demanding games out now, so performance on any integrated chipset built into an Intel processor is likely to be bad.