For one thing, that statement you quoted is completely unsourced. Sentences on either side of it are sourced to a book called "Chinese Whispers" [0]. It's a book about China, not about the etymology of English phrases. The author only discusses the possible origins of the phrase briefly in the introduction, where he explains why he chose that title for his book. He suggests the "Great Wall of China" explanation and the "mutual unintelligibility" explanation, but not the racist one(s). And he doesn't cite any sources anyway. It's just what he heard somewhere.
So we're left with just the fact that some anonymous wikipedia contributer says that this explanation of racist 19th century Britons has been proposed. By who? Based on what? Apparently not much. A different source I found points out that the earliest known use of the phrase in print is from March, 1964 [1]. Before that, it was known as "Russian Scandal" or "Russian Gossip". So it could hardly be the result 19th century attitudes towards the Chinese. If you're aware of any contradicting evidence, I'm happy to hear it.
Frankly, I wouldn't be surprised if someone came up with the racism explanation based on simply hearing the phrase and backsolving from their gut feeling that it was obviously due to racism. Then someone put it in a Wikipedia article without checking and now you're singling out that quote as an authority that vindicates your own initial gut feeling.
[0] https://archive.org/details/chinesewhispersw0000chub/page/18...
[1] https://www.phrases.org.uk/meanings/chinese-whispers.html