I've thought about this a lot and got into a lot of discussions about how golf is not a sport. (For golf to be a sport, we have to consider golfers - picture Tom Weiskopf or John Daly - athletes. I can't do it!)
John Kruk said himself, "I am not an athlete, I am a baseball player." So yea, it is a pretty hard line to draw between sports and athletic competition.
Activities require more skill then physicality and intellect. (figure skating, golf)
Sports require more physicality than intellect and skill. (Boxing, track and field)
Games require more intellect than skill and physicality. (Chess, Scrabble)
Most things require a combination of the three (especially team sports) but one of the three usually prevails. Baseball is hard to classify, for example. Fielders mainly use skills, pitchers and batters use a combination of physicality and skill.
Baseball is very hard to classify in your system, but harder, maybe, is football. I don't really like the game, but I have to say it is the ultimate test of all three of these skills (well, maybe boxing as well). Depending on the position you must master at least two of these. The quarterback must be reasonably physical, but hell of smart and skilled. Receivers and running backs must be the same, but more physical (fast). The linemen must be physical (strong), have intellect (know what holes to open for the running back, blocking schemes, etc.) and skill (the actual ability to block the defender). They same goes on defense. The linebackers are basically the quarterbacks, the defensive backfield the receivers and the defensive linemen the linemen.
This got me thinking, where do you draw the line between skill and physical ability. Most of the time one must have the physical ability to master the skill (or in bodybuiding, the other way around), most athletic activities are a mixture of both.
And I think bodybuilding is a mix between skill and physical ability. The skill is just really easy to master, compared to the physical ability one must have.