B"H
Today's Rambam, H. Rotzeich 5:4 says
וְעַכּוּ''ם שֶׁהָרַג אֶת הָעַכּוּ''ם בִּשְׁגָגָה אֵין עָרֵי מִקְלָט קוֹלְטוֹת אוֹתוֹ שֶׁנֶּאֱמַר (במדבר לה טו) "לִבְנֵי יִשְׂרָאֵל":
When one gentile kills another gentile unintentionally, the cities of refuge do not serve as a haven for him, for the above verse states: "For the children of Israel."
What would we think the cities of refuge "save" him from?
There's no example of the cities of refuge saving one from a court punishment, only the goal hadam ("blood redeemer"), as Ibid:9 says:
רוֹצֵחַ בִּשְׁגָגָה שֶׁהֲרָגוֹ גּוֹאֵל הַדָּם חוּץ לִתְחוּם עִיר מִקְלָטוֹ פָּטוּר שֶׁנֶּאֱמַר (דברים יט ו) "וְלוֹ אֵין מִשְׁפַּט מָוֶת":
When a blood redeemer slays a person who killed unintentionally outside the Sabbath limits of his city of refuge, he is not held liable, as Deuteronomy 19:6 states: "He is not judged as liable to be executed."
But it doesn't mention the court being able to kill him before reaching the city, but not after.
Furthermore, in a case when one is saved by the altar from a non standard court judgement, Ibid:14 says that if it's a real court case with witnesses (in the case of an intentional case by a Jew), then the altar (and obviously, a city of refuge) doesn't save him:
אֲבָל מִי שֶׁפָּחַד מִן הַמֶּלֶךְ שֶׁלֹּא יַהַרְגֶנּוּ בְּדִין הַמַּלְכוּת אוֹ מִבֵּית דִּין שֶׁלֹּא יַהַרְגוּהוּ בְּהוֹרָאַת שָׁעָה וּבָרַח לַמִּזְבֵּחַ וְנִסְמַךְ לוֹ וַאֲפִלּוּ הָיָה זָר הֲרֵי זֶה נִצָּל וְאֵין לוֹקְחִין אוֹתוֹ מֵעִם הַמִּזְבֵּחַ לָמוּת לְעוֹלָם. אֶלָּא אִם כֵּן נִתְחַיֵּב מִיתַת בֵּין דִּין בְּעֵדוּת גְּמוּרָה וְהַתְרָאָה כִּשְׁאָר כָּל הֲרוּגֵי בֵּית דִּין תָּמִיד:
When does the above apply? When one is obligated to be exiled. If, however, a person feared that a king will have him executed as is the king's authority, or that the court will execute him as an immediate directive, and fled to the altar and held on to it, he should be saved.
This applies even if he is a commoner. He should not be taken from the altar to die unless he was sentenced to death because of the testimony of witnesses who delivered a warning, as is always required with regard to those executed by the court.
So, when a non-Jew kills by mistake and is executed by the court, there's no reason to think that the city of refuge would save him from the court judgement, so seemingly this implies that we would think it saves him from another non-Jew who is a goal hadam.
But is there any source that says that a non-Jew can be a goal hadam, and therefore be exempt from punishment for killing another non-Jew (who killed his relative)? Seemingly, if this is the case, there should be an explicit source for it.