Actionscript is very cool and fun (I've done lots myself) but to be honest a concentration on "online web games" sounds like the latest fad to me. What I would recommend is that you strengthen the "classics" of Computer Science (algorithmics, operational research, C, C++, OOP, etc) which, once you know them well, should allow you to pick up any other language or technique that comes along.

Of course, you can always learn C++ on the side and apply the cool graphics techniques you learn for Flash into a C++ app, which would make your game/multimedia thingie it much faster and more impressive on a portfolio.