Pulled this out of the Application Log in Windows Event Viewer:

Faulting application name: TKOM.exe, version: 1.0.0.1, time stamp: 0x520ddb6e
Faulting module name: unknown, version: 0.0.0.0, time stamp: 0x00000000
Exception code: 0x80000003
Fault offset: 0x55cbffc2
Faulting process id: 0x17d0
Faulting application start time: 0x01cea12233f9df63
Faulting application path: G:\Program Files (x86)\Steam\steamapps\common\Take On Mars\TKOM.exe
Faulting module path: unknown
Report Id: 3c4b9a81-0d1c-11e3-be8e-a271b5481c9e
Faulting package full name:
Faulting package-relative application ID:

I am experiencing the same issue except that I'm running Windows 8 64-bit. I have attached my DxDiag file.

I have a workaround to this issue. If the game is run in Windows 98/ME compatibility mode, the game will run and play. However, the mouse will not operate as expected. When running in Windows 98 compatibility mode, the mouse will not allow for UP or RIGHT movements in DirectX 3D environments. They get processed as DOWN or LEFT signals. If the game is fixed to allow operation without compatibility mode, the mouse issue should go away (This can be reproduced in other non-BI games, if such games are run in Windows 98 compatibility mode)

Just a thought.. Are you one of the people running the game in Windows 98 compatibility mode? If so, this is why the mouse is causing problems. I have a report of this added to Bug ID 0000290