As Angela noted, it is my understanding that nicotine increases cell growth.
For instance, they are currently testing a nicotine lotion in California on the skin rashes of diabetics that could lead to amputation. They are hoping that the nicotine in the lotion will help regenerate cell growth.
So as Tropical Bob noted, it is possible that the mouth of a smoker has pre-cancerous growths already, and the chaffing of the gum and then the accelerated growth by nicotine, could lead to this.
There is also the smokers paradox. Smokers paradox is they are finding more and more that people who have been long time smokers who quit, end up getting cancer within the next 5-10 years. I don't think there have been any studies on this, I am sure if there have a few members could provide further detail.... However, one thing would be interesting to know if in these cases of smokers paradox, were they on other types of nicotine such as the gum or the patch or the inhaler.
In my grandmothers case, it was the inhaler and the gum. 50 years smoking... no cancer... lungs clean as a whistle. Quit smoking because she was sick of everyone nagging her... sucked on the gum and the inhaler like a race-horse and at year 10 of being quit... suddenly gets lung cancer which ravages her entire body within a year flat.