I'm not sure I find Ruth's explanation particularly useful.
The answer depends on whether you are using these as adjectives (don't use "a"/"an") or as nouns (do use "a"/"an").
He is American. Is this an adjective or a noun? Answer: adjective, maybe he was born and raised in Japan and is therefore Japanese, but currently holds US citizenship. He is an American (noun).
They are American. Is this a noun or an adjective? It's an adjective, the plural (they) noun is "Americans": "they are Americans".
This follows for all nationalities: European Europeans, Canadian Canadians, Kenyan Kenyans EXCEPT in the case of -ese (Japanese). While Japaneses is technically correct (it is in the dictionary), adding -s to -ese sounds wrong in English and so Japanese, Maltese, Chinese etc. all stay the same. To further complicate matters -ese words can't be used with a- or an- unless the -ese word is an adjective.
I am Japanese. They are Japanese. Both of these can be nouns or adjectives, and where they are nouns they are automatically either singular or plural depending on whether they are used with I (singular), you (singular), you (plural) etc.
I am a Japanese, he is a Japanese, she is a Japanese. These are all incorrect.
I am a Japanese person (the "a" attaches to person (I am a person) and therefore as with the description above can be used), he is a Japanese person (correct), she is a Japanese citizen (again correct because "a" attaches to "citizen" and not Japanese, she is a citizen).
Does this answer your question?