Is describing someone as "rikham" (meaning annoying, tiresome, or apathetic) considered backbiting (ghibah), especially if that person is absent at the time of the description, or if it was said in a moment of anger?

Gheebah (backbiting) is when you mention about your brother something he dislikes in his absence. If what you say about him is true, then you have backbitten him. If it is not true, then you have slandered him. As for disparaging him in his presence, that is an unlawful insult and vilification. Your statement about a Muslim, calling him "rakham" (a derogatory term, roughly meaning 'annoying' or 'thick-skinned'), is considered forbidden backbiting, even if said in a state of anger. You must repent, seek Allah's forgiveness, and apologize to your brother if your words reached him. Otherwise, supplicate for him.