The definition of jihad is the internal and external struggle to morally and ethically to do the right thing for the betterment of mankind and yourself. The only people who disagree are terrorists since they use it to justify violence and bigots who indirectly give credibility to the terrorist.
'The betterment of mankind and yourself'. This also includes violent oppression of anything that isn't Muslim. Muhammad himself fought bloody wars with his army and forced defeated enemies to convert to Islam.
I sincerely doubt that's how it happened.
Anyway, we still should kill Erdogan before he makes things worse.