There are two issues here. Firstly is your perception that they are 'quite mediocre, or above average at best' - this is your problem. Looking down on people for being less than yourself is not an admirable trait, something you seem to share with them.

The second issue is the other person 'tend to put down others who are more humble/less confident in their skills'. This is a what you would call a jerk (or arsehole in UK parlance). This is the issue that needs fixing. Are you in a position to call them out on this? Not necessarily official manager type position but pull them up each time they do it.

Someone like this could be seen as a bully and making the workplace unpleasant for the quieter / more humble members.

Their skills are irrelevant, if they were the most brilliant programmer in the world this would not excuse such behaviour.