I realize topolect is a translation of an official chinese term, but as far as I'm aware we're not Chinese officials. We're speaking English, and we can be brave enough to call mutually unintelligible languages what they are - languages.
And before anyone gives me the 'language is a dialect with an army and a navy' - yes it's pithy but there's so many counter examples.
By the way, I'm a linguist (and a native Cantonese speaker) who is acutely aware of the dialect/language issues surrounding our topolect, so while I sympathise and thank you for recognising that Cantonese would in other times and places be considered a language, using "topolect" allows us to focus on the topic at hand.
I'm not super familiar with the specifics of Mandarin, so I could be wrong here, but it's quite common to come across English words that have fallen out of common use by native speakers but are adopted by non-native speakers as a vehicle for expressing a concept that exists in their native language but doesn't have a precise translation into English.
Especially since they're talking about the evolution of Chinese pronunciation, "topolect", while jargon-y, seems to be a far more precise vehicle for expressing their sentiment.
https://en.wiktionary.org/wiki/topolect
http://sino-platonic.org/complete/spp029_chinese_dialect.pdf
It's a way to take 方言 and decouple it from linguistic terms like language and dialects so a proper study and classification of the Chinese language family and its various languages and dialects can take place without interference from Chinese politics. When someone points out that Cantonese, Hokkien, and Mandarin are 方言 then linguists can nod politely, agree that they are in fact "topolects", then continue classifying them as Sinitic languages within the Sino-Tibetan language family each with their own collection of dialects.
Would be interesting to know if the study of Arabic has similar issues because from a layman's cursory knowledge Arabic has similar diversity when it comes to mutual intelligibility.
On a side note, I actually found it a little bit ironic that Afrikaans was listed as a dialect of Dutch in his paper.
Many South Africans would disagree with that classification quite strongly, especially since Afrikaans has its own literature and regional dialects.
In turn, there's a movement to classify the coloured dialect of Afrikaans as its own language (Kaaps), in fear that it will be swallowed up by the more standard "white" form and erode their cultural identity.
It's a weak, flimsy word for people who know better, but still don't have the courage to say 'language'.
It's actually very similar to "topology" as a construction - "lexis" comes from "logos".