I'm not exactly sure. Sometimes newer games can be optimized for low-power graphics cards. Something like a software/hardware mixed renderer with tiling. Unfortunately Unity (the engine Clone Drone uses) doesn't support much in the way of any of these techniques, and is limited somewhat by the OpenGL codepath.
It's not terrible but it does require some hefty gpu fire-power at times. Switching to the Fast graphics preset can help a little, I think you can hold ALT at startup to set the graphics options before the scene loads.
Another thing with that graphics chipset is that it doesn't support the required version of OpenGL. The minimum system requirements include a shader model 5.0-capable graphics adapter. - Some intel IGP chipsets support Shader Model 5, so this could explain why a different computer might run it, even though it has no "graphics card."
Anyway, it looks like an upgrade is in order, if not for anything but a smoother OS experience. Sorry I couldn't be of more help!