This small shrine, located a little off the yamanobenomichi in Sakurai, Nara, is the legendary site of the first Sumo match between humans. The mythical origin of Sumo is in a contest between kami in Izumo. Izumo features in the legendary origin too, as the Sumo Shrine enshrines a man from Izumo, Nomi no Sukune, who was the victor in this first bout.
The story is set during the reign of the Great King Suinin who ruled over Yamato during the early 4th Century. There was a braggard named Kuehaya who lived over in Taima, across the Nara Plain at the northern end of the Katsuragi Mountains, who claimed that he was the strongest man in the world. Suinin heard that in Izumo was a man who was stronger, so Suinin invited Sukune to come and fight Kuehaya.
Sukune easily defeated Kuehaya, who died by having his ribs broken and his testicles smashed. I would guess that if contemporary Sumo went back to the traditional rules it would probably reverse its decline in popularity. In return for victory Sukune was given Kuehaya's land and invited to stay in Yamato and serve Suinin. Kuehaya and his fellows became the first makers of Haniwa.
Postscript: It seems there is some kind of unwritten law in Japanese media that forbids the use of the word "sumo" without prefacing it with the phrase "Japan's ancient sport of...". I guess that is to distinguish Sumo from the really, really, really, ancient sports of Roman wresting or Greek wrestling.