The claim in the article di that anger is associated with a desire for payback, of which revenge is one manifestation. This is subtle, but I think that in an article like this subtle differences matter. The author also claims that this is backed by psychology studies, though some sources for this claim would have been welcome.

The author does go on to focus on revenge only, and I'm with you on being skeptical that this implies that anger is an emotion that should be repressed. It seems to me that the authors equates a bit too quickly payback with a negative or a frivolous desire. The focus on Mandela's South Africa, of all things, is pretty curious since there definitely was a change in status for the white community after he took power.

When you're angry with yourself (or perhaps when you are angry at a situation in which you are by your own fault) the payback would be to not let that situation happen again. Or maybe the payback is to change yourself to address the character flaw that your anger is targeted at.