As suggested try compatability mode.
Not sure what the issue may be, but I had no problems with CoD2 (retail disc) on my x64 system.
I can not remember if I needed compatability mode though ....
My Computer
Computer Manufacturer/Model Number
Custom (Self Build)
OS
Windows 7 Home Premium 64bit
CPU
Intel Core i7 2700k
Motherboard
eVGA P67 SLI
Memory
8GB Mushkin Redline Ridgebacks @1866
Graphics Card(s)
EVGA GTX570 SC
Sound Card
XiFi Titanium HD
Monitor(s) Displays
LG W2453V
Screen Resolution
1920x1080
Hard Drives
Intel 320 80GB -- Intel X25-V 40GB --WD Black 1TB x2 -- WD Blue 640GB