Formulaic yes, a rule - silly, but it is useful to understand that putting your subject smack bang in the middle is not the only way to do it. I always like another rule of thumb (that I call the "L rule"): it's when you position a subject far to one side, then use a vast expanse of nothing on the other side to provide a balancing visual weight. Such as a tiny figure in the landscape to one side balanced by a mass of billowing cloud in the rest of the frame. There are many compositional possibilities and at least the 1/3rds thing introduces the concept.
I have to laugh how rigid and prescriptive some people get, though, about composition. Back when I was a camera club member, I submitted an image of a weird sculpture. It was kind of like a simplified stainless steel tree that had glass globes hanging from the branches like some kind of sci fi mechanical fruit. Mine was a close up of 4 of these glass fruit hanging from a branch with a deep blue sky as a backdrop. The judge told me it would have been a good photo if there had only been 3 glass bulbs, because photos look better when things are in threes...
I guess the problem of compositional guides, is that some rule-bound people think the guides are a kind of "checklist of goodness" that has to be passed, like a QC list. I'd like to think that people who become judges would be flexibly minded, but apparently not often the case.