The name Dancesport seems apt to me, not because of the physical demands, but because of the competitive atmosphere, which does encourage cheering and waving, and the presence of physical activity.
There are many activities, such as lawn bowls and darts, which are undoubtedly sports, since they are competitive pursuits with physical activity being a component. Now with those sports, there is little need for strength, and much less need for stamina than in dancesport, but there is certainly a need for physical skill. As there is in dancesport.
There are also activities such as ballet and bricklaying which require considerable stamina and/or strength, but without the competitive element we would not call them sports.
(There might be non-competitive recreational activities with physical activity that are regarded as sports, but I can't think of any.)
Basketball need not be called 'BigballSport' since the game itself must be sport, since it is always competitive and physical. So it would never need a name change for people to regard it as a sport.
Having said all this, I must admit that I initially recoiled when I first heard the name DanceSport. But that was because I think there is something inherently a bit silly in dancing competitively, although I have often done so happily! I just find it strange that our main goal seems to become competition results, rather than artistic reward. (The man that Strictly Ballroom was based on said a similar thing to me 8 years ago, but that is another story.) Also, the name 'dancesport' used in ballroom dancing ignores single person competitive dancing, such as highland dancing, and other partner dancers such as Swing, unless they also use it. But it still seems a reasonably clear and useful name; it is certainly simpler than 'competition ballroom dancing' or 'competition partner dancing'.
(This is my first post for a long time; I have been lurking too long, not being sure what to say! Thanks for all your work, Jonathan and Melissa.)