Depends on how the program allows itself to be managed. Many programs that aren’t multithreaded will still make use of multithreading if Windows is able to properly manage its use.
Even if the program is stuck without multithreading, it will always benefit since multitasking is an inherent task to a Windows operating system. One core will be taking stress off the other to keep Windows running, which allows for more available to the game.
Also, the newer multiple core processors will often have more cache and faster hyper transport.
Multiple cores always helps in some manner.
As a side note: This processor also won’t allow you to make use of “XP Mode” in Windows 7 (no virtualization).