You ask about "billiards" not "pocket billiards". There is no difference in the British or American version. A billiard table has no pockets. All three-cushion games are the same. All balk line games are played by the same rules. Now if you are talki...
well, it takes skill, practice, balls are involved, you use lots of muscles and its very competitive. i would say it is a sport.
I play ice hockey, so there might be a bias. Field hockey is NOWHERE near as fast as ice hockey. It's like soccer with a stick. Why does ice hockey worry you? Female leagues are actually non-contact.