The best definition of the difference between a sport and a game I've ever come across is that a player can smoke during a game. Clearly, rugby is a sport...who would want to be at the bottom of a ruck with a cigarette in his mouth?
By the same token, golf is a game. When I played golf and smoked...many years ago for both...I never had a problem with strolling along a fairway puffing merrily and the cigarette could just be thrown on the ground during the few moments taken for every swing of a club!!
Anyone who remembers when you could smoke in pubs, will recall how smoking darts-players could perfectly easily do both simultaneously. Darts is a game!
Having said that...keep the girls walking on, as long as the choice of doing so is theirs!