You quoted something from the thesaurus?

If you look at the dictionary (like you should), not every definition has overly in it or unjustified. Being the best at everything or not, or bragging about it or not Kei is definitely arrogant. He calls Hikari Miss 2. And when he came out to defend Hikari in the afternoon he said "There's no use talking to their kind."

He's definitely arrogant, fact of him being the best at everything or not.