If you're referring to noise cancelling headsets specifically, then I'd say there are few to no gaming headsets that have active noise cancellation (ANC). Any headset made primarily for gaming use, where the user will want noise cancellation, they'd have to rely on a closed headset with good isolation. I suppose in general, few gamers need something that has ANC. A lot of gaming headsets are expensive enough as they are. Add ANC to that and they are going to get even more expensive.
Difference between headsets designed for VOIP use and those designed gaming, will mostly be the size. Gamers generally want some kind of positional sound locating, which works better with full size over ear headset. For VOIP, nothing like that is required, so they are smaller on ear type headsets.
No reason why you can't use a VOIP headset with ANC for gaming, but it won't compare to something that is better designed for gaming. If you just want plain stereo though and have no want for positional placement effects, then a VOIP headset will do the job.