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.
This is more or less correct, ~1/137 corresponds to zero momentum transfer (or equivalently infinite distances).
This is because of screening by particle-antiparticle pairs at larger distances. See e.g. the first few slides of http://www.fysik.su.se/~clement/teaching/emparfys/2010-2011/... (one of the first things I found in a quick search).
