I believe it is relevant, because if the intent of making hush money payments was really to protect Trump's campaign rather than his marriage or his personal reputation (ha ha), that's what would make them illegal. If they were just a personal expense, then the campaign finance laws don't apply.
And this is where I think Ziggurat's argument is. If there is any slightest hint that it might have been for personal or business reasons - even if it was overwhelmingly for campaign reasons, they seem to argue that no crime has been committed.
This seems to be a very minority view. And of course, there is probably a reasonable chance (maybe 50:50) that the there is actually an email trail discussing the effect of the buried stories on Trump's electoral chances.