Ming is a character that Rowley did for many years live at the Groundlings. He was in various sketches in different formats- sometimes it'd be a normal sketch and other times it'd be an interactive improv where Ming was a life coach and he talked to the audience, etc. etc.
It's worth nothing that at that specific theater, you have to produce several sketches a week with new 'big' characters every week and they encourage you to use any tool you can to create a character- pick a piece of wardrobe, a voice, a physicality, etc. and try and turn it into a character. In that fast-pace process, sometimes it can wade into murky waters when the character shows ethnic or flamboyant traits. It gets murkier still when you do a ethnic/flamboyant voice or behavior and the audience goes wild for it. Some performers will cut something if its problematic even though it gets a great reaction and other performers will double down on it. Stand ups have a similar problem when they're trying to write new material quickly- some cut jokes that don't fit their worldview, others will keep anything that gets a consistent laugh.
With all that said, the incarnation on CBB seems to be just an irregular and specific accent or cadence for Rowley to use while riffing. Without knowing that it's a remnant from an actual character or seeing Rowley perform it (he has a Jim Carrey-like rubber-face when performing), it is pretty much a voice which I can see as being insensitive/offensive/confusing.