The perceived loudness option in the loudness meter is based on the International Telecommunications Union's ITU 1770 standard. The ITU have performed experiments that show that this is a good measure of perceived loudness. The European Broadcasters' Union have based their recommendations on this measure of loudness as well. So while it's trying to measure something that's not possible to universally define like loudness levels, it's not a random thing.
But what really did it for us were the listening experiments we did ourselves.
While a meter bar certainly has its own advantages, its position is not as easy to remember later as a number is. We chose to make a numerical display because we wanted people to check out the levels of the tracks they like and easily remember those numbers in the future without having to go back.