Is Islam synonymous with ISIS and Taliban, to a jingoistic xenophobe?
I think the better question would be (if you were dealing with someone reasonable):
If ISIS were not in control of this place, would this have happened?
Rewind the tape to the 90s, and you had this sort of thing happening under Taliban rule in Afghanistan. Public executions, extreme oppression of people, repression of anything remotely modern (dress, music, pop culture, etc.) and generally strict enforcement of religious mores.
All imposed by the Taliban, and all gone once they were deposed. During all this time, the religious demographics didn't change. Afghanistan was Muslim before the Taliban, Muslim during, and Muslim after, so Islam wasn't the problem...it was the Taliban and their weird extremist interpretation of it that drove the behavior.
For this incident to be blamed on Islam generally and not on ISIS, you'd have to show that stoning of 15 year old gay teenagers (with the crowd being forced to play along) was commonplace before ISIS was running things.