The misalignment of definition comes from misunderstanding of words.
From the very beginning of Chinese writing, writing is not word by word record of spoken, but specialized form of record eliminating any unnecessary redundancy. This makes Chinese writing more independent from actual pronunciation of languages and allows the evolution of languages without affecting Chinese writing much. It is no surprise that Japanese, Korean and Vietnamese has adopted it for a long time with this adaptable structure.
《方言》 is a book written nearly two thousand years ago, which means the words of various places (in the empire).
When Western linguistics was introduced in Chinese, "方言" was chosen to mean "dialect". While a dialect means a mutually understandable branch within a language, some perceives it is various speeches in China.
It is pretty tricky that while the Chinese writing is understandable across languages but the speakers of various languages are not mutually intelligible in daily life. The political issues on the unification and nationalistic climax of China causes widespread misinformation of 方言.
Nowadays linguistics agrees that they are Chinese languages and linguist groups them in a Chinese language family. Only those with no linguistics knowledge would still debate on the word 方言.