Pool is a sport according to ESPN, the National Sporting Goods Marketing Association, to Sports Ilustrated and every definition of sport that exists.
Now I see where most of your problem is. You don't respect the sport.
According to the World Games billiards is a sport.
http://www.theworldgames.org/the-sports/sports/precision-sports/billiard-sports
Billiards is recognized by the International Olympic Committee as a sport.
Billiards is a game in the same way that basketball and baseball and tennis are games and a sport in the same way that they are sports.
The comparison to golf is actually quite relevant as both activities are fairly low aerobic ones, both require great body control to hit a stationary object in the desired direction. Both require the player to navigate tricky situations.
And both have lots of methods with which to attack the goal. Including aiming methods.
http://www.aimpointgolf.com/
https://www.youtube.com/watch?v=ZQQ...;cycles=-1;autoreplay=false;showoptions=false
https://www.youtube.com/watch?v=1PD...;cycles=-1;autoreplay=false;showoptions=false
https://www.youtube.com/watch?v=7e8UgT6LrW4
I love the internet. It's so awesome.