Yes, conkers is sufficiently well-known enough as a children's schoolyard game that I would expect pretty much every newspaper-reading adult to have heard of it. The fact that there is supposedly an "adult" championship event would be a surprise to most. If you're looking for the "story behind the story", other than the fact that it's a seasonally-specific, light human-interest story: there is probably a slight cultural bias amongst those who most fondly remember the game towards the private-school-educated, upper-class types who combine nostalgia for imagined "glory days" with political conservatism, so this is a good opportunity for the left-leaning Guardian to hand-pick someone who appears to belong to that class and expose them as a ridiculously-dressed scoundrel with childish interests and suspect morals. The subtext is: these are the sort of idiots we want you to associate with Nigel Farage, Boris Johnson and co, and thus the Overton Window gets a tiny nudge in the opposite direction.