1920x1200 is actually 16:10. You might think of that as 16:9 plus a little a horizontal strip for a menu or toolbar.
Anyway, if the game supports widescreen, then it often in theory supports 1920x1200. But that's a lot of pixels, and you need a fast video card. There are other variables, like the complexity of the game itself, how much antialiasing you have turned on etc. The 6600 is pretty good, but certainly not top-of-the-line. If you can get acceptable frame rates for a given game at 1920x1200 using DVI (with the desired quality effects like antialiasing, water, smoke, etc.) it'll look really nice
But the rule of thumb about sticking to the native resolution is primarily so that text and icons look sharp and not smudgy. With a 3D game, it's not as important, since all the pixels are calculated anyway. Ideally, you'll still want to play in widescreen -- if in fact that mode allows you to see more. So you might choose a lower 16:10 resolution, like 1680x1050.
If the game doesn't support widescreen, then the monitor should just center the picture instead of stretching it. If you can play the game at 1600x1200, it will fit the native resolution of the monitor. Anything else will scale.
The bigger issue with LCDs and games is pixel response time.
