The Rambam explains the basic requirements of doing teshuva and seeking forgiveness from another person: acknowledging the transgression, making amends, and seeking forgiveness (presumably publicly per Yoma 87a). If a person wrongs us and does these things, we're to forgive him. (He also has to not do it again, but that's for God to judge later, not for us.)
There is, nonetheless, a "release clause" in the Yom Kippur liturgy, where we forgive even people who haven't done this so that no one should be punished on our account. This answer on another question points out that this explicitly excludes people who owe financial damages and people who transgressed knowing we'd have to forgive them. I can't say why exactly, but I've always understood this passage as being about fellow Jews -- a Jew who has wronged me non-financially, and didn't do it knowing I'd have to forgive him -- I forgive even if he didn't do teshuva, because we're all imperfect and if we're favorable to others maybe God will be favorable to us. I am not sufficiently fluent to be able to tell if the passage quoted there actually says "anybody at all" or means just klal Yisrael.
So my understanding is: if a Jew does teshuva we forgive, and if a Jew doesn't do teshuva but these other conditions are met, we forgive anyway.
A non-Jew, by definition, is not participating in this mutual "release clause" on Yom Kippur, nor is he bound by the laws of teshuva. So, two questions here:
According to Judaism, what, if anything, is a gentile required to do if he wrongs a Jew? (We have laws about Noachides, so halacha might have something to say here.)
If a gentile has wronged us and not done anything about it, is he included in our blanket forgiveness or not? Does "anyone" mean anyone, or just Jews? If I make no specific exclusions, have I passively forgiven a gentile who's wronged me or is he not part of the scope in the first place?1
In both cases, does it matter if the gentile is a Noachide, an idolater, neither, or of unknown status?
1 I don't know if it's actually kosher to make exclusions -- to say "except Ploni" -- but it happens sometimes.