You want to know if you have understood this tweet correctly:
Well done on reducing one of the greatest sportswomen alive to racist and sexist tropes and turning a second great sportswoman into a faceless prop.
Hope you don't mind but I'm going to ignore your suggested interpretation because it didn't really make sense to me. I'm going to dismantle the original tweet from my point of view as a native British English speaker.
I feel that anyone would need to know the context to understand this completely. You mention the "cartoon" in your alternative version, so presumably you are aware, but for the benefit of any other reader: JK Rowling was stating an opinion about a cartoon published in a newspaper which depicted tennis players Serena Williams and Naomi Osaka. The cartoon has become highly controversial because critics say that Serena Williams is portrayed in a "racist" and "sexist" way. Supporters of the cartoon say that this is just representative of cartoon caricatures in general, that they just exaggerate anybody's physical characteristics in order to make them identifiable and look ridiculous for the purpose of parody or satire.
"Well done" here is being used sarcastically. Even if that wasn't clear from the outset, it becomes apparent as you read and see that well-known feminist Rowling is "praising" someone for sexism.
Looking at the first part of the tweet:
..reducing one of the greatest sportswomen alive to racist and sexist tropes..
JK Rowling is essentially condemning the artist firstly for "reducing" Serena Williams, who Rowling regards as "one of the greatest sportswomen alive" to a caricature which she says is "racist" and "sexist". For reference, Serena Williams is the main feature of the cartoon, appearing in the foreground in great detail. She is portrayed as having a massive child-like tantrum, and there is a child's dummy (or 'pacifier', US) on the floor to suggest that she has just "spat it out". "Reducing" someone suggests that everything good about that person has been stripped away leaving only negative points to focus on. One critic was quoted as saying "her humanity is stripped from her in order to accentuate her Blackness being synonymous with her anger".
... and turning a second great sportswoman into a faceless prop
The "second great sportswoman" is Naomi Osaka. She is not "second" in the sense that she is less great than Serena, but just that Rowling is speaking about her second. I understand the term "faceless prop" to mean that the cartoonist put her in the background of the cartoon, where firstly you can't really see her face, and secondly she does not say anything. All the "humour" of the cartoon is meant to be derived from Serena's outburst and a "quip" from the umpire. A "prop" is literally something inanimate in a stage play or a movie, such as a chair or a table that an actor may interact with or even just stand in front of without interaction. When a person is referred to as a "prop" it usually means that they were just there to complete the look of a scene rather than actually participate in it. It seems to me that Rowling's complaint here is that while Osaka's portrayal may not appear "racist" or "sexist", it is a misuse of a sportswoman she believes should be celebrated rather than confined to a "prop".