You can use a ton of laptops for gaming, I don't know what they are talking about. Desktops are just more recommended because you can get more power out of them, obviously when your working with more space like that, your going to gave more power options. But yeah, Nvidia or ATI for the most part. ATI drivers suck though fyi.
I got to disagree with you Most laptops have integrated gpu and you cant really play the new games with them.
While I don't use a laptop, I have plenty of customers who use them to play games.
Most older RTSs (Age of empire, starcraft, Warcraft 2 etc.) will run fine on any somewhat recent computer. As far as newer games, I'd just give them a go. Most games you can download a demo for. Get it and see how it runs.