I believe it is important to make a firm distinction between what people commonly think is true, and what is actually true. While distinguishing them, both are useful and valid information to make note of.
Chinese is a group of multiple languages, just like the slavic language group or romance language group. Some places in the world have a Chinese language as an official language of the place: Mandarin and Cantonese are two off the top of my head chosen as official languages of areas. This is not different than English being the official language of some places, and spanish the official language of others.
Many people think that Chinese is synonynous with Mandarin: This is a valid observation, although what many people are thinking is incorrect.
Just as many people think that everyone in south america speaks spanish: all sorts of languages are spoken and portugese is very high up there in reality. Or how many people think of knights with swords in the middle ages and soldiers with guns post industrial revolution: guns were around in the middle ages too in reality.
The article notes a common misconception, which in itself is good information.
P.S. There is standard chinese as well, a written onpy form, used by most different chinese languages in mordern day. It is read out loud differently in each language but can be understood by all chinese speakers who have learned it. This is how you have those who don't know cantonese understand a text from hong kong etc. (For the record it is based on Standard Mandarin I believe, although it varies a little).