It means that he plays a game that sort of looks like golf, but fails to meet the definition. I read it as if you are ahead, you can give your opponent a mulligan out of the goodness of your heart, but if he subsequently moves ahead in the match at some point, he is required to return the favor. Not surprised you didn't quite get it as it's a new one on me too. Guys like us who play by the real rules often don't learn these odd rules setups.
...unless I'm misinterpreting Fourputt, which is certainly possible.
All I'm doing is giving the rules answer. His game does not meet the definition of the game of Golf as it is stated in the rule book. I wish that there was a better terminology that didn't always get people's hackles up, but the only true definitions and answers which apply to the game are in the rule book. If you look up the word "move" in Webster's, you get a very different definition from the one in the Rules of Golf, but the latter one is the only one which applies when discussing the accidental movement of the ball in Golf. When rules topics are raised on the forum, the only real answer is the one in the rule book. It's hard to always have to differentiate between Golf by the Rules and just golf, and I know that it sometimes sounds demeaning, but the difference is there, and as in this instance, that difference often has to be pointed out to answer the question as correctly as possible.
When anyone mentions playing in a scramble, they usually preface it with some reference to not playing by the rules and nobody gets upset because we all know that the scramble format is not recognized by the Rules of Golf. Yet when anyone talks about this or that rule modification and how to deal with some problem, they ask as if they are playing by some rule, yet they aren't playing by the rules, and the only answer that can be offered is the one in the book. That means that someone is going to get their feathers ruffled since the question may or may not even apply to Golf by the Rules. I know that I come across as stiff and unyielding, but that is because the rules are stiff and unyielding. If you ask some of these questions of a USGA or a PGA of America rules instructor, you will get a terse answer, or maybe no answer at all other than that the question has no answer since you aren't playing by the rules.
I have stated repeatedly that I don't care that many intentionally don't play by the rules, but that doesn't change the fact that when a rules question is put forth, the answer must come from the book. Unfortunately, there is sometimes an insurmountable barrier between a discussion of the game of Golf by the Rules and discussion about golf modified for casual play.