Never used nicotine gum or tablets but found they contain peppermint oil, an artificial sweetener and menthol, and that may be the source of the peppery flavor in those products. That is a sweet peppermint flavor found in the candy and gum shelves, which is different from the "pepper" flavor associated with cigars. Pepper flavor in cigars is more like the pepper that is in the spice rack: black, white, cayenne, chili. And pepper in cigars is distinguished from spice flavors: cinnamon, licorice, anise, cumin, nutmeg. So "spicy" does not mean "peppery" when talking about cigar smoke.
Some cigars, like the Cu-Avana Pvnisher Intenso, are actually coated or infused with capsaicin or other form of pepper oils to deliver a burn to the lips and tongue and to impart additional pepper flavor. I often put the cut head of a cigar on my tongue to get a pre-light taste of the tobacco and usually taste pepper and get a slight burn, so it seems to me that unburned tobacco can taste and feel peppery. Once lit, however different cigars produce different flavors, and pepper is only one flavor in the "taste spectrum."
Even though a the cigar's tobacco may taste peppery on the tongue, it may not produce a pepper flavor in the smoke. The variety of types of tobacco and places where it is grown, the amount of time the leaves are aged/fermented, the part of the plant the leaves were taken from, the climate and soil composition in the region where the tobacco is grown, techniques used during fermentation all yield tobaccos that produce smoke that has a unique flavor profile.
Everybody has a unique palate, so you may detect some flavors in a cigar's smoke which I don't. And there are some flavors that I appreciate more than others, and they are different from other people's "sweet spot flavors." Personally, I don't taste a lot of cigar smoke flavors in my mouth, unlike many other cigar smokers. The method I use to "taste" (smell, sense?) the subtle and nuanced flavors of cigars is by the retrohale, where I slowly let the smoke drift through my sinuses and out the nose.
Here's a link to a "flavor wheel" that has included the various types of flavors that have been detected in cigar smoke. Some cigars may produce only 2-3 of them, while others may produce 5-6 at various stages of the cigar's burn. The more flavors produced, the more complex the cigar.
http://www.cigarinspector.com/cigars-101/cigar-flavor-components