The rambam.you quoted is, as not surprising…wrenched out of context. He does not say “non jew”, he says akum, which is in contrast to the lines above your quote where he says that it appears to him that a ger toshav receives chessed like a Jew. Then he says that even an idol worshipper receives tzedaka, visiting their sick and burying their dead, because of darchei sholom. See Taz on the shulchan aruch seif that you quoted that explains that there is no connection at all between the giving lf tzedaka to goyim and to Jews, by yidden it’s a mitzvah and by goyim it’s just darchei sholom.
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