I play pool at a pretty high level. Local hall down the street was ran by Mexican legend Francisco Galindo. Saw him play Keith McCready, former number one player in the world, for 20 thousand. Now that I got my "cred" out of the way, yes, it is a sport.
Anything in which physical execution is just as important as mental execution (i.e. strategy) is a sport. You can't arbitrarily set the number of "athletic" events you want to see in a sport and then define or dismiss based on that criteria. I can say, "they don't run around in full team volleyball, its cardio demands are just a little over walking, (180 calories in 30 minutes. You burn about 140 in 30 min at a brisk pace), it's a non-contact sport, so therefore I deem it not a sport!"
Number of athletic events is meaningless. They occur, and when they do occur, you need world class athleticism to meet their meet their demands (any sport at the pro level).
And what is an "athletic event" anyway? Another arbitrary determination based on taste. Nailing a 150 yard golf shot from the rough, fading it around a tree, and landing it 5 feet from the pin is just as "athletic" as some action that requires "running around."
Your logic is pretty terrible.