I don't know about drugs. Ego, messiah complex, and delusions of invincibility? Sure.
Putin got where he was through reality-TV-level ostentatious displays of strength. Prigozhin likely figured he was the only one who could boast measurable gains in the war, and the same tactics would work for him.
My guess is his miscalculation was assuming he was more popular among the rank-and-file Russian military and police than he is, and it's too early to tell if that's actually a miscalculation.
Another possible explanation: he got the backing of some faction inside the Kremlin, but they did not really back him when push came to shove.