Why was Ebisu killed by the Pacification Ring?
I have two theories to why Ebisu was killed by the Pacification Ring.

First is that the Ring is just a energy cannon that is meant to exterminate the enemies of heaven. Therefore, it not only affects Ebisu but also those around him. Quoting from the wikia,


  Pacification Ring, a form of punishment to destroy enemies of Heaven.
  
  
  


Second, he was not 'pure of heart'. We can take the words the other gods said to mean 'pure' by their standards and not Ebisu nor our standards. Therefore, Ebisu, who has committed sins against heaven, is not 'pure' of heart, according to the other gods, who cast the ring. This god here said that what Ebisu did are taboos and we can infer that by the standard of the other gods, Ebisu is not 'pure' of heart anymore.




  As Sigfried666 also mentioned, in the manga, Ebisu is killed by Takemikazuchi's Kiun. Therefore, the ring is an anime only event and may not have any logical justification.