The reason Hiking is not classed as a sport is because it is non-competitive. The Olympic Games does have paced walking as an event, but that isn't Hiking. Neither have I ever seen or heard of Hiking footrace events.
Having said that, hiking is a strenuous activity, particularly on hilly or mountainous terrain. Many hikers, such as myself, combine endurance with the joys of sightseeing and photography. You don't do these things when competing in a race!
But to take hiking seriously, an element of training is necessary to build stamina. One of my life's greatest hikes was one I completed at the Grand Canyon in 1995. There I hiked the Bright Angel Trail down to the Colorado River, then on to spend the night at Phantom Ranch right at the bottom of the Canyon, then hiked back up to the Rim the next day, a total hike of 23 miles, taking in a three-mile detour to visit Plateau Point for the extra vistas. This hike was extra strenuous because it is the reverse of mountain hiking. At the Canyon, the uphill part is last, when one is already tired!
For training, two or three times a week, I went out to break in my new hiking boots by walking up to ten miles in an evening. Added to this, I spent a weekend hiking the Jurassic Coast Path, (in the UK) which has some crushingly challenging hills, some steep enough to virtually crawl on all fours (honestly, I'm not exaggerating!). When I arrived at my hostel bed, my whole body was aching, as I carried a backpack throughout the hike. But the preparation paid off.
If ever you hear of a hiking footrace, let me know!