I had this exact same problem: Win7x64 system, AMD video card with latest Catalyst drivers. I have it working now and this is what I did:
Added Overseer.exe to the DEP whitelist (right-click My Computer for properties > Advanced System Settings > Advanced Tab > Performance Settings button > Data Execution Prevention tab > Add Overseer.exe to the list ). I had DEP turned on for all programs and services except those I select:.
I downloaded the June2010 DirectX End User Runtimes directx_Jun2010_redist.exe from microsoft I ran it and it unarchived itself to a folder of my choosing and then I ran the DXSETUP.exe file. Then I downloaded the the DirectX Web Install package dxswebsetup.exe from microsoft and ran that too.
I downloaded and ran the latest ffdshow x64 setup from sourceforge and selected all the codecs to use libav.
Finally, in the Catalyst Control Center for my AMD card, I went to 3D application settings (Gaming tab on left menu > 3D Apllication Settings) and added (+ Add ... under the Application Settings in the window) an entry for Overseer.exe. I set it to override all the application settings and basically turned everything off that I could (Anti-Aliasing Samples = None, Filter = Standard, Anti-Aliasing method = Adaptive multisampling, Morphological Filtering = off, Anisotroic Filtering Level = 2X, Texture Filtering Quality = Standard, Surface Format Optimization = Off, Wait for Vertical Refresh = Off, OpenGL TripleBuffering = Off, Maximum Tesellation Level = Off).
That got the game running. In the game menu the audio is set to Microsoft Midi Mapper and in the video is set to the hardware renderer.
I don't know which of those steps actually did it, but now the game is running at least up to the first day in Tex's office following the FMV, and the office textures look right and the object interactions works.
Yay. Hope that helps you.