That will depend on your GPU more than your CPU. The CPU adheres to the same x86 architecture intel has been using since the 8086 (plus new features) and the windows operating system (ABI + API) both adhere to a subset of the instructions for maximum hardware capability.
The core 2 duo will can only parallel process 2 threads simultaneously as intel had not added hyper threading architecture as they have now. For comparison, the i7 will allow 8 multiple threads (2 on each of 4 cores) where the i5 has no hyper threading so 4 multiple threads (1 on each of 4 cores)
Having only a core duo will be a significant performance impact in the case of gaming where there are many different engines (sound, video, physics, save state, realm loading, etc)
That said, the largest, most visible impact is going to be your GPU, which you can think of as a very very limited CPU designed mostly to perform floating point operations (arithmetic on fractional binary numbers) very very fast. These chips have almost zero branch prediction and are designed primarily for rasterizing vector graphics to your screen. They have (depending on the chip) upwards of 1500 "cores" (calculation units) aboard.
You should pick an appropriate GPU for the game. The integrated graphics in the Core 2 duo will not be sufficient. But with a graphics card and the core 2 duo you should just be able to scrape by.
When building a computer, you should a lost always sink as much money into the CPU as possible. GPU you can get away with mid-upper range range (~$400-600) since the market prices for absolute best are ridiculous ($2k for little improvement over 2 of the $600 SLId together)