Earlier quoted context omitted.
I always find the claim that dialects in China vary so much that people cannot understand each other very western-centric. As a native speaker, there are shockingly few dialects that are completely incomprehensible. Someone from Shanghai will be able to speak to someone in Chengdu with their own dialect, just slower.
Take Cantonese (or heck, Teochew or Hakka). You really think this language is reasonably mutually intelligible with Mandarin? Or Shanghainese? I'm a (non-native, formerly fluent but now pretty poor) Cantonese speaker and I'd describe the difference between Cantonese and Mandarin as roughly the difference between Portuguese and Romanian. Sure, they're both romance languages, and maybe with a lot of work and hand-wavin…
Have you ever watched either Ip Man or "The Bridge" (Danish/Swedish cop show)?
In Ip Man, there's a gang of Mandarin speakers who show up in Ip Man's Cantonese world. They somehow are able to speak to each other, and I find it unlikely. Perhaps it's because my Cantonese is mediocre. But it just doesn't sound like you could have a casual conversation across the languages.
A similar thing happens in The Bridge. There's two cops solving a crime on the bridge connecting Denmark with Sweden, and they just talk to each other in their own languages. My guess is most people who didn't study the other language would not know all the slang, as importantly the simple expressions. Though I guess it could be learned easily; I can read a Swedish newspaper, just not process it fast enough to have a fast conversation with a colleague.
Similarly with German and Swiss German. Something about the way the sounds are different makes processing the other one a bit slow if you're not used to it.