Don't give up on your dream just because some random guy on the Internet tells you to. (An advise from another random guy on the Internet)
addictinggames.com is a flash game website. If you want a shortcut, you can start learning flash/actionscripts. If you want better basic (really want to be a programmer), then you can start from C++/Java/C#.
There seems to be a few books on Amazon on flash gaming:
Amazon.ca: flash games
Start with something really simple, if you like it you can move on to something bigger.