Not sure if I was racing or not...

No, you weren't racing.

I've run through race packs before.  It often gets some raised eyebrows as I was obviously coming through the back of the pack doing the pace that people in the front were.  So I spend half the time saying "I'm on a training run, I'm not in the race.  Run your own race and good luck!"

I also have to say no.

IMO racing is not just about the actual race itself but also about the mental aspects of it, which you only get if you do it for real.

X2.  And the corollary is that you can sign up, start with the race, run the course, finish, and still not be racing. I did that yesterday, running a 1/2M because for personal reasons I wanted it to be my first 'race' back after surgery, but I didn't want it to mess up my training.  So I did the 'race', but didn't race it.  (Towards the end I couldn't resist and ran hard, so maybe I raced part of it, but the first 7-8miles were at training pace.)

Originally I did not really think of myself as racing, more like pulling a version of Rosie Ruiz, except I was never actually a participant in the race, and did not try to cross the finish with the racers. I figured since I did not start with the others or cross the finish line, I really wasn't racing.  But in terms of the mental aspects, I think I raced as much as I ever do when I am actually in the race.  At one point there was a trail that had a clump of people moving slowly.  I could have adjusted my pace to maintain myself in a lower HR, but I ran to the outside and passed them.  At another point, I noticed my HR was up in the top of my zone, but I calculated to myself the distance I had left to the "end" (not the official end, but my end point) and kept the pace up. So I think if racing is defined as the mental game, I was racing as much as if I was actually registered.