I'm going to answer the question with "no", it's not racing. Auto crossing is you all alone, driving as fast as you can as the only driver on the course. Are you competing with yourself and trying to improve? Yes! Are you competing with your previous time and trying to go faster, brake and steer more efficiently? Yes! Will you finish the day and compare your solo time with other driver's solo times? Yes! But are you really "racing" the other competitors? That's up to you!
You can have a race with your spouse on who brushes their teeth the fastest, or ties their shoes the quickest, but I wouldn't call that racing either. But if you just enjoy driving your car and being able to autocross at the level that pushes the capabilities of your car in accelerating, braking, cornering, steering, etc, then you will love auto crossing.
One description of auto crossing is that it is the opposite of every day driving. Well, for most of us it is the opposite, because every day driving means I'm trying to drive smoothly, safely, stay on the road, stay in my lane, and not be so aggressive that I wear out my brakes every week and only get 1 mile per gallon! Depending on how long you have been driving, you might have somewhere between 5-50 years of driving like that, so when you put on your helmet and fasten your seat belt for an autocross, a lot of that mentality goes out the window. I figured out last year that I had to FORCE myself to be more aggressive, especially with braking and cornering. Cornering is probably where I need to improve the most, because while it's fun to have your tires squealing around a corner, (and sound like a chase scene in a "Dirty Harry" movie), that squealing sound is probably really a waste of tire grip making the car go sideways instead of forward and faster.
This weekend will be our first autocross of the season, and we'll be out there driving hard, being safe, having fun, and at least for me, the only racing will be to see if I have a faster time than Brian at the end of the day.