I’m not quite sure who you are referring to, but if it is Hoffman, he indeed is a Republican. If he doesn’t win this special election, he will run in the next primary as a Republican. He will go on to win the seat :-)
He ran against the RNC backed Republican candidate. It doesn’t matter what he IS but how he RAN. This flies in the face of conventional wisdom by splitting the Republican vote and giving the Democrat the win. By doing so and beating both the Republican and Democrat candidate fires a shot across the bow of both parties.