Well, from my non-physicist's understanding of the matter: the fine structure constant is associated with the strength of electromagnetic interactions. The value we call the "fine structure constant" that's about ~1/137 in the equations is the lower bound of that strength, the strength of the interaction when you're dealing with energies about the same size as the electron mass. However, when you're dealing with higher energies, the interaction is stronger.
The interesting question as far as I can tell isn't related to how electromagnetism's strength varies over different energy scales, but whether the strength of electromagnetism at a given energy scale varies over time or space.