Divinity Original Sin
Divinity Original Sin is a true Kickstarter success story. Far pass its financial success though, it is also a very solid, old-school RPG with good characters, deep and varied combat and a wonderful world to explore. You do lose a part of that when playing with Intel integrated graphics, but not enough to badly impact the experience.
A very quirky survival title with a Burtonesque art feel and style, Don’t Starve is a smart game to play either by yourself or using the standalone multiplayer expansion, Don’t Starve Together. It’s not very demanding on your system, so it is playable even with older integrated graphics chips.
FTL: Faster Than Light
A hard roguelike with resource management, branching, as well as randomized quest events, FTL: Faster Than Light is a fabulous indie game that is far from hard to run. You will be able to run it on any sort of integrated graphics chips with no difficulty at all, though higher resolutions could benefit from a slightly faster chip.
Kingdom: New Lands
Kingdom: New Lands is a really simple game that can use up hours of your life if you let it. Its pixelated graphics look great on powerful and older hardware alike and all you need is a graphics chip with DirectX 9.0c support to run it. If your processor is a little weak, you might encounter some slowdown in the later stages of the game, but most of the gameplay will be smooth, even on integrated graphics.
Five Nights at Freddy’s Series
For an easy premise, the Five Nights at Freddy’s series of games are astonishing spooky and full of jump scares for folks who love a good fright. Since they aren’t really visually intensive, they play very well with onboard graphics chips and there are lots of them to play through if you like this type of gameplay.