It might work, but on the other hand, it's a pretty dangerous world. A fighting tournament is inherently easy because everyone in that world understands fihting skills are highly useful. For sports as we know them, you need a world where people can afford to spend a good deal if not most of their time for developing skills that may not be useful for anything but that sport. Not to mention, it would need to be a sport where being a non-human of some kind doesn't automatically make you a winner with little effort. Fighting can be done in myriad ways, so there are no automatic losers there. However, if you are throwing a javelin or running 400m, following a strict form and rules, humans would need to be exceptional with unique skills to beat mediocre mosters born with a magical physique. This is an issue because Rimuru, being a former human, really likes humans and wants to remain involved with them.