This is an interesting claim to make. Up until quite recently (I mean that in the usual sense of the word, not the AI world sense of the word), almost no one had heard of Anthropic or Claude, despite an reasonably aggressive ad campaign, even at the point when most people would have known about ChatGPT.
Even now, I would guess that if you ask a normie off the street, they are far, far more likely to have heard of ChatGPT than Claude. Of course, Anthropic has been targeting businesses quite a bit harder than the general public for a while, so maybe that's not a fair test.
Anthropic inarguably does make an attempt at marketing their product. But I'm not convinced that the closing of the gap between them and OpenAI (as others have pointed out: I'm not sure it's defensible to claim that either is significantly ahead of the other given the paucity of available data, but they are certainly much closer than they were a year or two ago, when OpenAI was clearly in the lead) is mostly down to that. I think that, for a decent chunk of time (this one I mean in the AI world sense of the term), they had a very non-trivial lead in coding abilities. The developer and business world figured this out and jumped on board. That gap is largely now erased, but that's not enough to retake the momentum.