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…
See e.g. this video: https://www.youtube.com/watch?v=Ps7_NnkL-oM where for almost the entire video a couple is explaining words in their respective dialects (Sichuanese and Hunanese) to one another in their own dialect (i.e. not using Standard Mandarin at all in their explanations). The first half of the entire exchange is fluent and understandable by both people and also a Standard Mandarin audience. Only in the second half when they intentionally start quizzing each other on words they know will be tough for the other person and without additional context do they run into trouble (and occasionally resort to Mandarin).
Also, comparing it to Romance languages masks some complexities of the relationship. https://news.ycombinator.com/item?id=16844074