Licinius, the more you explain your position, the more I think you're reading something into the current wording that just plain isn't there. Saying Aussie Rules is an Australian variety of football does not say that it is more Australian than "gridiron" (NFL is the competition, not the game!) is American. It doesn't say that Australians haven't had great influence on rugby league. The descriptions of the sections don't need to be, and in fact shouldn't be in the same format, since the different groups are not exactly the same sort of groups. The different codes are grouped into sections based on their history and similarities between the codes. There are two very obvious big groups, both easily characterised by their "ancestry" - the kicking games descended from association rules and the carrying games descended from the rugby rules. The rest of the codes, all relatively minor in global terms, cannot be characterised by a single ancestry, and so shouldn't be. They are a group of games, some influenced by both soccer-type games and rugby school rules, with various influences within the group as well, that are most easily characterised by the fact that they are all Australian or Irish in origin. Saying some of them are Australian varieties of football is not saying the rugby codes are  "unAustralian" any more than calling Gaelic football an Irish variety implies that Irish soccer players are not Irish/Gaelic!