Long before you were born, and long before they started making automobiles, the Daimler-Benz motor company put a motor on a wooden bicycle. Thus, some time around 1880, the "motorcycle" was born.
Throughout their lifetime, these "motor cycles" have performed many tasks: as transport for mail carriers, explorers and mappers of the American West, troops during wartime, etc.
But, more importantly, they were quite popular for their ability to give people enjoyable personal transport. At one time the number of companies in the Unites States making these "motor cycles" numbered in the dozens Names like Mertz, Pope, Ace, Reading, Indian, Excelsior, Mercury, DeDion, etc. were seen on the gas tanks of what today would be considered "standard" or "naked" motorcycles.
These motorcycles did more than just road duty. The United States Army commissioned a platoon of motorcycle soldiers shortly before WW1 to test the ability of motorcycles to move cross country as a group. Imagine riding your 250 across an open field of grass, let alone riding a bike with about an inch of suspension travel.
In these early days of motorcycling, anyone interested in owning or riding a motorcycle had to have a certain amount of knowledge about the mechanicals of the bike. It was not just gas-and-go like today. An owner had to know about changing tubes in tires, troubleshooting engine problems, maintaining the bike, etc. In today's world, the equivalent would be a biker who changes his own oil, spark plugs, chain, tires, valve adjustments, suspension tuning, along with riding and polishing.
Even after WW2, similar traits were seen among riders. In order to be a biker, you had to know many things about the bike, and in many cases the owners took to modifying their bikes based upon their understanding of the bike's functions.
In those days, it was decided by people far more insightful than yourself to call non-competitive recreational motorcycling a "sport". It wasn't just a hobby, because one was actively engaged in motorcycling, from riding to maintaining the bike. That, and it wasn't something that persons with sedentary lifestyles were attracted to, as many hobbies are. And is wasn't quite recreation, because riding a motorcycle is a very physical, sweat-generating activity as well as the probability of the bike breaking down at the least opportune moment and needing labor to get back underway. Yet another aspect supporting the "sport" moniker is the fact that to be proficient, you must be engaged in learning about the craft of motorcycle riding, consistently expanding your abilities and skills, and not just a passenger like so many people driving automobiles.
So there is much more to calling motorcycling a "sport" than just randomness or marketing, which is what might be garnered from initial examination.