Being an avid boardgame player, I am pretty competitive in that area - I have been, since a kid. I am also a musician, and funnily enough, I don't feel I am competitive in music at all - my outlets for music tend to be much more collaborative and sharing.
I am currently somewhat obese (although being over 6' tall, I carry it better than some), but even when I was thin and reasonably fit, in my 20's and 30's, I was not competitive athletically. Although I still fondly remember a time when some college friends nagged me into going on a run with them, promising to take it easy for their slacker friend. I started off lagging behind, but then got into my pace, and ended up passing them all, to their shock. But while I found it immensely amusing, I didn't find running or any kind of sport interesting enough to pursue at all - it bored me.
With regard to cooking - be it BBQ or otherwise - I do it because I absolutely love it. Anyone who meets me will assume I do it because I like eating, but it isn't that - I love learning new ways to make things that taste nice, and I love surprising guests (I guess that is competitive, no?). I also love tinkering with tech, which is why I have more cooking and BBQ kit than a single guy should need.
I can seem me competing in BBQ some time in the distant future, but I have a need - a compulsion, really - to know exactly what I am doing before doing it front of others, particularly those more expert than me. I know this is usually not necessary, and I will learn more by making mistakes in front ot others, but I can't help how I am made. This is probably a strong sign of a competitive spirit, in that I will only want to compete when I have a decent chance of competing on even terms!
I haven't answered you questions directly, but I think my answers touch on the same subjects. Hope it is of interest.