It is no more a sport than dominoes or fun fair hoop throwing. It may be great entertainment but that doesn't make it a sport. Physical as well as mental skills are needed for it to be classed as a sport. In my career I need to work hard, have good concentration and do better than the man next to me. But I do not consider my work a sport.
Darts is the same.
Just because it requires these skills doesn't make it a sport. The participants are out of shape, lazy people who drink too much. There are two sides to every story. Yes, darts involves overweight men exerting no physical effort with the only sweat being the result of the lighting. So, it's not a sport in the sense of athletics or swimming, but to class it as entertainment is way off the mark.