alt Hacker NewsCantonese is a language, yes, but mutual intelligibility and similarity to other languages is hardly relevant unless the languages are very similar indeed.
For example, there are spoken varieties of English that are mutually unintelligible, while speakers of different Slavic languages are often capable of having a good conversation by speaking slowly and listening carefully.
In practice the main criterion for being a language as opposed to a continuum of dialects is the degree of standardisation. So an example of something that may or may not be a language might be something like Swiss German (but I'm not an expert so I can't guarantee that's a good example). Another type of borderline case is when you have two standardised languages which differ only slightly, for example US English and GB English, or DE German and AT German.
> For example, there are spoken varieties of English that are mutually unintelligibl
Which? I have travelled to, worked in, or lived in multiple countries with English speaking populations (by which I mean some people speak English as a first language, though it may be a small minority) on five continents and never had a serious problem understanding people. Some slang and idiom and loan words, but thing much.