So just chewing NRT gum releases the nicotine?

Yes. NRT gum is a nicotine-resin complex. When the gum is chewed, cations in saliva, for example sodium, enter the gum and exchange with the nicotine contained in the resin. This releases the nicotine into the saliva. This is why you do not want to eat or drink while using the gum because this would result in you swallowing the nicotine-laden saliva and may upset your stomach.