The first appearance in strange sports stories might be the first account of camel wrestling. This is a traditional sport in some regions where two male camels are made to wrestle against each other. It's a very unique and somewhat controversial sport as it involves animals. But it has been around for a long time and was surely strange when it first came to people's notice.
Quidditch from the Harry Potter series could be considered in a way. Although it's fictional in the books, real - life Quidditch has emerged as a strange sport. The first appearance of the idea, even in fictional form, was quite novel with players flying on broomsticks and trying to catch the Golden Snitch. It inspired people to create a version on the ground with modified rules.
I think the first appearance in strange sports stories could be the start of the Cooper's Hill Cheese - Rolling and Wake. It's an annual event in England. People roll a large cheese down a hill and then run after it. It looks completely mad. People tumble, fall, and get bruised all in the name of chasing a cheese. This must have been a very strange sight when it first started.