You can play Friar Tuck or you can play a friar, Tuck. Notice the difference. For most native speakers it is ungrammatical to use play X where X is anything but a proper noun in English. Common nouns work differently.
You can “play God”, or you can “play a god”, but you cannot “play god”, which is miswritten. That’s because the last is an error in orthography revealed by the actual grammar.
Proper nouns and common nouns are two closely related but grammatically distinct parts of speech. Since these differ grammatically, you can (in most cases) distinguish one from the other when these form part of a spoken utterance.
As proof that this a distinction grammatical rather than orthographical, I present to you several sentences normalized to all capital letters and no punctuation. You will see that the proper nouns nonetheless remain completely identifiable bereft of any hinting.
- MARY CALLED MOTHER AN ANGEL
- MARY CALLED HER MOTHER AN ANGEL
- MARY CALLED HER MOTHER GERTRUD
- MY SISTER CALLED OUR MOTHER GERTRUDE
- SISTER CALLED MOTHER GERTRUDE
- SISTER MARY CALLED MOTHER GERTRUDE
- HE SAID THE JUDGE WILL SEE YOU NOW
- HE SAID JUDGE JONES WILL SEE YOU NOW
- HAS THE MILKMAN BEEN BY YET TODAY
- HAS MIKEY BEEN BY YET TODAY
Whether something should be capitalized as a proper noun is a writing effect driven by real grammar.