Chinese is traditionally only written. A Chinese person would speak in his local dialect, but read and write in Chinese. The local dialect typically had a different vocabulary and grammar from written Chinese. Since these dialects aren't written, only spoken, they're dialects.
Largely due to politics, over the last two centuries written Chinese has gradually shifted such that nowadays its grammar and vocabulary have a one-to-one correspondence with a particular dialect, namely Mandarin. But that wasn't always the case. Indeed, most ancient written Chinese poems don't rhyme in Mandarin: but they rhyme in many older dialects (like Cantonese).
Now stuff like Tibetian: that is a language, separate from Chinese and with its own writing system. This is not the case for Cantonese (and 40 other major dialects in China).