I think a better way to explain would have been that Qo'nos was destroyed and without a unified homeworld the Klingons just descended into infighting which then lead to a destructive fight-to-the-death, civil war over resources. Wochak is the leader of a House that refused to fight in the war, knowing that it would be the end of the empire. A few other houses joined him and formed a fleet of survivors.
Wochak has tried to find a new homeworld that all Klingons will accept but has been unable to do so. Faan Alpha is the answer to his prayers in being identical to Qo'nos. Faan Alpha gets painted as a new chosen world that the spirit of Kahless has lead them to or some such. But to get all the Klingon houses to agree and unite, Jay-den makes the same suggestion he does in the episode.
Wochak has tried to find a new homeworld that all Klingons will accept but has been unable to do so. Faan Alpha is the answer to his prayers in being identical to Qo'nos. Faan Alpha gets painted as a new chosen world that the spirit of Kahless has lead them to or some such. But to get all the Klingon houses to agree and unite, Jay-den makes the same suggestion he does in the episode.