Yes, having a dedicated graphics card is important if you're looking to game. However for the games you play (Gmod, Worms, Minecraft, etc) you won't exactly need a high-tier card. A low-mid tier card would be more than fine for those games.
In your situation it would be difficult to find a proper dedicated graphics card in a laptop. At $450, you simply won't find a laptop with one. You're likely going to get the integrated Intel 4000 or 4400 at most. Which those integrated does fine for some games but you're going to play on low settings. My friend has an Intel 4000 and he plays GMod relatively fine. It's at low settings and lowered resolution too. So keep that in mind. It's likely the same for the other games. I do not think MW3 will run at playable rates to be honest. You're going to miss out on games at $450 laptops. It's just how it is.