I have a competitor that is # 1 across a few competitive terms.

He/she has anchor tags which are basically self-link tags, referring in different ways to the very same page they are on (keyword rich)

Isn't this discouraged when done like this or is it A-okay?

As far as links back to the same page they reside on, I don't think that those carry much weight in the algo...chances are the other linking and content is what is providing the number one rankings...

Basically, all links are beneficial, as long as they aren't "spam." (many would argue that those are too-to them I say "for now!" :p ) This is why some people develop PageRank without even having inbound links.

If a site has content using keyword rich anchor text that leads to further relevant content on opther pages, it cannot really hurt. When it is done in excess it simply looks bad, IMO. It could also eventually cause penaties but not yet as far as I have seen.