I've been a daily nicotine gum user for years, and I'd say I'm addicted. I've tried to quit several times. I'll kick it for a couple of months, and then I'll have a stressful week and I'll buy a box. Then I'm back on it for a couple of weeks until the box runs out. And sometimes I just go buy another box.
For me, it's not addictive in the sense of "I experience withdrawal symptoms", but I have very strongly conditioned habits with specific triggers. Nicotine spikes my dopamine, and also improves my concentration and memory when I'm using it. Which makes me like it, and also chemically encourages situational cravings.
As an example, I chewed it when I was driving to work every day for a while - and now I think about it almost every time I drive anywhere. It's not really an "I need a piece right this second" kind of feeling for me, but more like a "Man, some nicotine would be awesome right now" kind of feeling.
One aspect of the addiction that I think many nicotine users would agree with - it's not an instant process. I knew I was developing the habit long before it was a full-blown addiction. I kept telling myself I wasn't going to get addicted, that I was stronger. Turns out maybe not so much.