Game mode bypasses most of the image processing a LCD TV does to give you the best image quality. Which results in pixels on your tv refreshing ever 2 milliseconds or so. Still, CRT TVs do that in less that 1 millisecond.
The difference is trivial. Besides, everyone should be playing on LCDs by now, no? What's the point of going on a CRT when it's basically extinct?
CRTs are the standard.
So far, every big Melee tournament run have CRTs at every setup.
The lag's not as trivial as you think