As /u/shakespeare-gurl and /u/SeiShonagon mentioned in a past thread, the Emperor of Japan was not really seen as a living god until the Meiji period, when the new government set about heavily promoting the divinity of the Emperor in order to use him as a unifying symbol for the nation. Prior to that, there was the idea that the Imperial line descended from gods, but not the belief that the Emperor himself was a god.

As the Boshin War took place before this happened, the people fighting against the Imperial forces would not have seen themselves as fighting against some sort of god. This is not to say that the imperial throne wasn't an important political symbol in Japan prior to the Meiji period - it was - but it wasn't a "divine" one in the way that people popularly imagine it to be.

Quite a lot of the ideas that are popularly associated with Japanese culture and history are really ideas that were only formalized in the Meiji period and onwards - the God-Emperor, "state Shintoism," and the concept of bushido were all notions used by the government to foster nationalism in Japan.