This photo, for example, shows a plain old plug-in iron: https://web.archive.org/web/20161017222702/http://teamsteam....
Same guy, up in a tree, with the same iron: https://web.archive.org/web/20161017223140/http://teamsteam....
From this page: https://web.archive.org/web/20160920083532/http://teamsteam....
¯\_(ツ)_/¯
If ironing is just about extra bulk of equipment not the actual product of ironing, then it's more like weight-added competition. Otherwise there needs to be some way of judging the ironing aspect, like quality, novelty, or artistic merit, in addition to the otherwise difficulty, like in figure skating, for example.
But just for fun - everything is sport. In the line of "everything and the kitchen sink", how about extreme dish-washing!
Apparently the clothes don't need to be dry either!