Yes, pretty much so, because of the modern design of having everything packed in tight, coupled with the fast CPU's of modern machines, they can run quite hot.
This can be observed when using data continuously as with a game, and also just with modest usage once room temperature reaches mid 30 degrees C.
I'd say the aluminium is to some extent a heat radiator, and yes, it can get too hot to touch. I sometimes wonder what impact this has on internal components.
More than likely yes. Games put a huge strain on computer hardware. You should try to vacuum out the vents on the top and bottom of your iMac to make sure that there is proper air flow. When it gets hot do you hearthe fans speed up? You can also get a utility called iStat Pro to find out just how hot it's getting.