I have the LN-S4051.
There is no option to turn off DNIe.
It does still operate on OTA HD and component HD signals. I do not have HDMI connnected yet, so I cannot confirm nor deny that.
That being said, the effect is very subtle, at least with my picture settings. The biggest difference I see is that it reduces the red push of the set, making skintones more flesh colored instead of ruddy. Other than that, I don't see much difference and don't understand why all of the hoopla about being able to turn it off.
And yes, I do use the set for gaming on an Xbox 360 (Halo 2), and I don't notice any lag, either due to DNIe or otherwise.
I don't use Game mode (it's too bright and the colors overexaggerated), but with it on, DNIe still has an effect. With Game mode on, DNIe actually makes the colors more vivid, especially reds. This seems to be the opposite effect to what it does with Game mode off.