I have played sports all my life. Baseball from t-ball through high school and American Legion.
Football, from peewee up through high school and some college.
Up until about aeighteen months ago, I played hockey in a league that included guys who had played in the AHL.
I have coached Little League baseball and youth hockey.
In all of this, I have never heard of sports being seperated into "competitive" and "non-competitive sports".
There is no such thing. Something can be competitive without being a sport, such as cheerleading, professional bass fishing, bridge, etc. but it cannot be a sport without being competitive.