My intuition is that German, for example, is much less active of a language in the US, where immigration peaked long ago, than Chinese, where immigration is active.
This is enough to discredit the whole infographic in my eyes. No matter what the CPC or anybody else may claim, these are distinct languages, and not dialects. Not only that, but in some of these places a lot of Chinese speak other regional Chinese languages, such as Fuzhounese, rather than Mandarin or Cantonese. (I remember a blog from twenty or so years ago by a NYC Chinatown native who mapped his building by language; something like a dozen Chinese languages were spoken by residents of that building's apartments.)
I think you're right that Cantonese should be (and usually is) referred to as a "language" but the categories "dialect" and "language" are not mutually exclusive. For example, Dutch is both a language (for most purposes) and a dialect of West Continental Germanic (for some linguistic purposes).
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.