It's a bit more complex than that, and part of it includes understanding the euphamistic nature of language in Russia. He was actually a small time convict, petty theft, etc that got caught and spent time in prison all the way back in the 70s and 80s. Once he got out he opened a hot dog stand in St Pete, which is part of the whole chef thing circles back to. However, he wasn't selling hot dogs, the was his laundering operation; he was a drug dealer. Basically, he went from being sort of a small time gangster, went in the joint and came out with new skills. Of course all this was around the time of the collapse, so then it really became the wild west. Anyway, he went from the hot dog stand to being other business, usually in dinning and food services, in order to launder his growing enterprise.
At this point, he meets Putin, during a deal which was intended to relieve starvation in St. Petersburg, for $90 million USD, he and Putin orchestrated a fraud together to bilk this thru his food services companies. Important to remember this part, both of these fucking guys grew up there and had ties to the community, but instead of providing the food they should have to their own community, they just stole it and said screw them. Shortly thereafter, and if ever there is anything that sort of summarizes Russia, Putin gets elevated to Yelstin's second fiddle and the rest is history.
The Putin's Chef thing refers to two things. 1. Which is obvious is the food services, food contracts, and dining aspect. 2. The other is actually referring to his ability to launder money thru said food enterprises.
At the end of the day, Prigozhin was just a thug and a murderer. A generally awful human being. Fuck him.