No. "Gamma rays" in modern scientific usage has a specific meaning: radiation coming from the nucleus or from annihilation reactions (electron + positron is considered a gamma source despite not involving a nucleus), not from the electrons. The energy bands actually overlap, you can't always tell whether a given photon is without understanding it's source. (The lowest energy gamma rays actually fall in the UV part of the spectrum.)

And what they're saying is the energy of the lightning is acting as a particle accelerator. aka atom smasher. And there's a surprising level of atom smashing going on in the big thunderclouds.