I'm not a moderator here, but I see no problem with this.
This user sees him or herself as an expert on a specific topic relevant to our site. They've posted numerous answers that seem comprehensive and knowledgeable (at least on the surface; I haven't had a chance to read them in detail yet, and I likely don't know enough about Superman to accurately judge them).
I see no mention of their site in their answers, or comments, or anywhere besides their profile and username (and as PearsonArtPhoto linked in a comment above, the username is acceptable).
In short, the contributions this user has made so far seem exactly the kind of contributions we are supposed to attract: expert answers (with "expert" being understood as a rather nebulous term that can be interchangeable with "someone who spends a lot of time with the subject matter", for our particular site).
Note that some self-promotion is acceptable. The specific rules are:
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.
If a large percentage of your posts include a mention of your product or website, you're probably here for the wrong reasons. Our advertising rates are quite reasonable; contact our ad sales team for details. We also offer free community promotion ads for open source projects and non-profit organizations.
I see no signs of these rules being violated, or even approaching being violated.