Tosafos asks why the prohibition of a goy to bring an animal missing a limb isn't listed in the 7 noachide mitzvos? Tosafos explains that it isn't an issur, rather an obligation to fulfill his promise and redo the sacrifice by bringing a healthy animal. Both the Mishneh L'melech (Melachaim 10)and R. Akiva Eiger (gilyon ha'shas) point out that Tosasfos only makes sense if we assume that goyim are obligated to keep their promise, but where do find ba'al ya'chel applies to goyim?
See this link for a previous discussion about this issue:
The Mitzpeh L'eisan elaborates about the obligation of a non-jew to keep their promise. We find in the Midrashim that Yacov Avinu was punished for delaying his vow and was therefore punished with Eisav and the angel, and the suffering with Dina being kidnapped. Even thought the Avos kept the Torah, they certainly shouldn't be punished to such a degree for violating their promise unless they are obligated to keep their word. See also Torah Temima at the beginning of parshas Matos where he quotes a Sifri that learns out that a goy isn't included in the prohibition of ba'al yachel. The fact that we need a drasha to exclude a goy from the technical prohibition of ba'al yachel implies that he is required to keep his word.
In the linked post I pointed out that he commitment made by Har Sinai to receive the Torah can only be binding if the Jews were obligated to keep their word PRIOR to the acceptance of the Torah. See Tosafos in Shavuos 29a who asks what the point was of taking an oath to receive the Torah - כשהשביע משה את ישראל אמר להן דעו שלא על דעתכם אני משביע אתכם, they could just as easily violate the promise as they can violate the issur of idolatry? Based on the above, the question can be answered that the obligation for a human being to keep his word doesn't come from the Torah, nor does it come from the 7 mitzvos given to Noach. Rather, it is innate in the human being who was created as a נפש חיה = רוח ממללא. His very existence and ability to speak comes with the responsibility of מוצא שפתיך תשמור ועשית.