Well, I think that by any reasonable standards of "winning", Richard Dawkins beats just about everyone here, whether he agrees sufficiently with local tropes or not.

I agree. And that also means that whether he mentions Bayesian epistemology or not is not the best question you can ask. A better question would be, how could he have improved his output, or improve his future output, by mentioning or adopting it? The same could be asked about the Sequences.

...it's not clear I'm qualified to answer.

I think that a strong SI advocate would have to say that Dawkins is not "winning" because he did not conclude that risks from AI are the most important issue one could care about, even though he knows about the possibility of superhuman AI. So he must be below the level of SI standards. And by reading the Sequences he could learn not to waste his time with less important issues anymore ;-)