I consider them sports. They all take some level of physical ability, skill, and coordination. As well as have a competition.
Even heliskiing/boarding, now have competitions such as the Red Bull Supernatural and Cold Rush. Ski BASE, or any BASE jumping, does not yet have any competitions that I've heard of, but I don't really follow BASE jumping.
Ski Mountainering on the other hand, is far more physically demanding and challenging than heliskiing, basically because you have to get your arse to the top on your own, using many mountaineering disciplines in a single ascent. And it definitely is an extreme sport because most of the time you are against not only yourself, but the mountain and the elements as well. Enjoying such an activity/sport comes with a fatal risk, but that's what makes you feel more alive. Those are some of the most in shape and toughest people around. They may not be ripped, but they are undoubtedly in top shape/health.