The help centerhelp center has this to say about self-promotion:
Avoid overt self-promotion.
The community tends to vote down overt self-promotion and flag it as spam. Post good, relevant answers, and if some (but not all) happen to be about your product or website, that’s okay. However, you must disclose your affiliation in your answers.
Addressing each of the points in the rules:
"Post good, relevant answers": as far as I can tell, the posts do answer the questions, and the links are given for supplemental information.
"if some (but not all) happen to be about your product or website, that’s okay": as I write this, that user has written 15 answers, 6 of which link to their personal blog. I also see some links to other non-commercial sites (e.g. University websites), so it's not exclusively to their own site.
"you must disclose your affiliation in your answers": I didn't think this was perfectly clear in all of the earlier posts, so I edited them to make it clearer and left a commentcomment explaining why I did so. The user agreed to make the affiliation more explicit in future, and in the newer posts, has held to that.
tl;dr: At this point, I don't think there's too much for concern. Enjoy your nap!
