I agree with everything you said but also interesting to note are the roots of the whole situation.

For example during the 1880’s Chicago blacks were incorporated into both the First Ward political machine of the Irish or Coughlin and Kenna and the Second Ward organization of Republican Alderman Big Bill Thompson. Also Mushmouth never heard of the policy racket until Patsy King arrived, a white guy. Story goes that King was in fact the one who introduced first Sam Young and then Mushmouth to the policy racket since King already worked the racket on the riverboats while Young worked as a porter and then they met. Theres also another legend which states that a Chinese guy who allegedly went by the name of King Foo was also one of the first guys who brought the game. And so by 1903 Mushmouth, King, Young, Foo, with the help of another Irish gambling operator known as Tom McGinnis, controlled all policy wheels under the watch of Kenna, Coughlin and also King Mike. A lot of "Kings" during those days lol

Also by that same time period larger portion of the prostitution racket was locked down by the Jewish and Italian population (mainly non-Sicilian), and even the counterfeit biz. So I believe that some of the slave owners or racists one day decided to label the policy game as the black mans racket obviously because later they owned it, with the bad word being the original one, and even if the racket was placed mostly among the Chinese population, still it was going to be the same situation but with a different slur