The plugin works on several sites, there must be something blocking or conflicting with it on your site.
I can’t be much help without investigating your site!
But you can do a simple check to find out or narrow possibilities:
1- Deactivate all plugins, and switch to the default theme.
2- activate only the Author hReview plugin (make sure it’s working, and it actually should)
3- activate your theme ( check if the plugin is working, if not, then tell me what theme you are using)
4- activate all other plugins one by one, and check your site each time till you find the one that conflicts with Author hReview, and tell me which plugin.