I always figured anyone on a bike is a cyclist.

Once off the bike I'm not sure where to draw the line. Anyone making a living on the bike is still a cyclist as are many others.

EDIT: I'll admit to occasionally be tempted to call those on very expensive bikes wearing a full kit and riding a very easy route very slowly poseurs rather than cyclists. But then I remember the time I passed a woman cyclist who was about the 10th best in the states when she was cooling down after a ride. If I had not known her (and was a lot more concerned with speed than I really am) I could have mistaken her for those I am tempted to call poseurs.