The title from Gershwin Melody #31 seems as likely as anything to come from a tempo suggestion. Gershwin song sketches that never got lyrics or a title are often referred to by such non-title jottings and/or musical notations.
So feel free to play it slowly to give your audience time to appreciate the interesting harmonies woven throughout the piece. Or if you feel inspired, it could easily be played in a more spirited march tempo. Credit again goes to composer and Gershwin’s longtime intimate friend and musical confidante, Kay Swift, for notating this song. Swift would typically find these song sketches in Gershwin’s music notebooks, and she wrote down pretty much anything worth notating and filled in any missing harmonies as she remembered hearing them. Fortunately, she had a phenomenal musical memory, and her work on the Gershwin Melodies (also sometimes referred to as Gershwin’s “Special Songs”) was a labor of love and an invaluable service to those of us who treasure Gershwin’s music.