If one received a gift from a non-Jew of a non-kosher bottle of wine is it permissible to re-gift it to another no -Jew?
Regarding benefiting from the wine of a non Jew, the Sefardi minhag is to consider all wine made by gentiles to be forbidden even to benefiting from it, and it should not be given away to a gentile as a present. The Ashkenazi minhag is slightly different than this. The Rema bring different opinions, if nowadays the wine of a gentile is considered stam yanom and benefiting from it is permitted, or not. The Rema concludes that in order to prevent a loss, (i.e. to collect a debt from a gentile in the form of wine, when otherwise the Jew may lose he money owed to him), that one can be lenient. In your case it isn’t really a loss to throw out the bottle, because you didn’t pay anything for it. Therefore the correct thing would be not to re-gift it to a non Jew.
The Chochmas Adom (75-14) says that even in a case of loss it is preferable to be stringent, but he gives a bracha to those that are stringent that they should have financial success. Even though your situation is not one of a loss, you still have my blessings that by not re-gifting the bottle, you should have financial success.
Shulchan Aruch Y:D 123-1