I came across this statement. Is this correct? I am specifically confused at the part where "a" comes after "are".
Yes it's correct. People is a noun like any other. It can be a collective noun standing alone as in:
There were people everywhere in the hall.
Or it can be a singular noun, taking 'a' or 'the', referring to a race, nationality or culture of people. In this form it can also become plural - peoples.
The plural verb 'are' is used because it belongs with The Japanese [people], a plural collective noun. Compare:
American crocodiles are a species with the scientific name Crocodylus acustus.
Neanderthals were a house-proud race who liked to return to home comforts, fresh excavations of caves in Gibraltar have revealed.