I'd say anyone who is buying or making a new computer should strongly consider getting dual core. All software that comes out is being programmed to utilize them, including games.
Of course, there are always budgets to be met, and everyone has different needs. From what you have described above it looks like you have a "budget level" budget
If games are your priority, and you are on a tight budget, then the X2 3800+ may be your best choice, however, you are going to want a decent graphics card. The graphics card is (arguably) more important than the CPU for gaming. It would be more important to get a decent graphics card over getting a dual core CPU. An Athlon64 3200+ cpu and a 7600GT graphics card are a great match for budget level computer gaming.
You are going to want a good card for today's newer games, and personally I wouldn't want anything less than a 7600GT at this point but they are $200 canadian:
http://www.tigerdirect.ca/applications/SearchTools/item-details.asp?EdpNo=1931188&Sku=P450-7836
That aspire system you link to above has a very weak graphics card. You could always upgrade it in the future, but I am pretty confident that you'd be disappointed in it's performance.
Keep in mind that my advice is also coming from someone who likes to have all the game's "eye candy" turned on, and played at high resolutions. If you are OK to turn down your games' settings, and lower the resolutions then you can spend less on graphics cards, and still play your games.
I hope this helped.