Agreed. Game programming will teach you a lot of programming skills, and staying with game programming can elevate you to great heights as a programmer, and it's great fun.
The only negative is that games are relatively closed systems, whereas most of the rest of the software world includes a lot of interaction with other systems (databases, security, operating systems, payment etc etc) which you may never get to practice while programming games (unless you do multiplayer online games i guess).
Oh, and do not expect to earn money programming games.