There are exhibitions, teams, leagues, singles competitions, team competitions, national and international competitions; everything that you would expect an official sport to have. It has observer status at the Global Association of International Sports Federation and been recognized as a sport by half the countries needed to become an official Olympic sport. Is Jump Rope a Sport? - Here's What to Know | Elite SRS
I'm pretty sure there is no international association of stair stepers and that is supported in Strava so why not jump rope?