I agree with your point, and the parent's, that Valve's success is most directly caused by Steam runoff and their own sales dollars, and not necessarily their dynamic organization style.
...do many people think or claim that their success is due to their management style? More importantly, is that why we're talking about it? Certainly that isn't the focus of this Gamasutra summary of the EconTalk podcast by Valve's economist.
Valve does talk a lot about their org-style in general, and they do talk a lot about their success. But I'm pretty sure they have a sound, mundane reason for those things: talent sourcing.
Standing out in the tech industry as an employer is tough, and the traditional offerings: "smart people working on interesting problems", "we're growing fast", "we're the market leader" are, excuse the expression, tantamount to banal rape. Valve has a further difficulty though, as expressed by Varoufakis:
"In many occasions people simply don't fit in not because they're not productive or good people, but because they just can't function very well in a boss-less environment."
They need to find talent like everyone else, but beyond that, they need to find talent that won't fail without someone taller telling them what to work on. Valve's sane solution to both problems (lack of talent, lack of talent-preparedness for their org-style) is to get loud about their org-style.
Valve's org-style is so wild and different that it means we could all talk about it until the cows return -- and we do. They routinely make (tech website) headlines just by repeating themselves, which draws crowds. It also causes candidates to self-select, lessening the fit-problem. Don't think you'd like to work at a Place Like Valve? You won't apply. Never thought about this org-style before? You will now.
Why do we love to hear about their org-structure so much? Is it just because it's different, or perhaps because of apparent claims it's more profitable? I think it's because it addresses a real problem. It would appear that silly directives-from-on-high don't exist at Valve, because they internally removed the notion of "on-high". They also claim to have given each employee the autonomy to figure out how and where to do their best work, while being paid enough. It sounds like they struck the creative-work motivators of autonomy, mastery, and purpose[1] on the noggin. Good marketing at the least.
[1] RSA Animate's adaptation of Dan Pink's talk http://www.youtube.com/watch?v=u6XAPnuFjJc