The complete minimum requirements (taken from the box of the german retail version):
* Intel Pentium IV or comparable processor with 1.5 GHz and SSE1 support
* 512 MB RAM (Windows XP) / 1024 MB RAM (Windows Vista and up)
* video card: 128MB VRAM and Shader 2.0 support
(ATI: Radeon 9800 and up, NVidia: GeForce 6800 and up)
* integrated/onboard graphics: 128MB VRAM, DirectX 9 and Shader 2.0 support
(Intel: GMA X3200 and up, ATI: Mobility Radeon 9800 and up, NVidia: GeForce Go 6800 and up)
* DirectX compatible sound card
* approx. 4 GB harddisk space, keyboard, mouse, speakers
The problem is that the Intel GMA 3100 graphics don’t have hardware support for vertex shader. Have a look at the Intel graphics comparison chart: Link
Look at the 3rd generation in the line 3100. In the column Shader model (vertex/pixel) there’s the entry "3.0(SW)/2.0". The "SW" indicates that the vertex shader support is software instead of hardware. This means that the vertex shader code is calculated by the main processor using the graphics driver software and not by the graphics chip. A 100% accurate calculation by the main processor would be very slow. That’s the reason why NVidia/ATI started to let their graphics chip do it long before the more current Intel graphics cores also do it (one of the first with hardware vertex shader support was the GMA X
3000). So the Intel driver software for older Intel graphics chips like the GMA 3100 do a trade-off between performance and compatibility when it lets the main processor calculate the vertex shaders. The result is that this works with some games that needs vertex shaders while it doesn’t work with other games.
Black Mirror 3 needs full shader 2.0 support and uses vertex shader. When the game was released the Intel driver software was not able to calculate the vertex shader code Black Mirror 3 uses. It crashed with the error message Pete_N posted.
If your graphics drivers aren’t up to date you can tryto update them. Sometimes more current driver made the vertex shader calculation compatible with a few games that didn’t run before. But it’s not unlikely that the Intel driver software vertex shader calculation is still not compatible with Black Mirror 3.