Answer

I didn’t understand the question. What does “what is the binding force” mean? Are you asking from where they are obligated? From a divine command. See Maimonides in his Commentary on the Mishnah to Hullin 7:6, where in the end the binding force is from the command at Sinai. And similarly in Maimonides at the end of chapter 8 of the Laws of Kings.
As for the difference in punishment—I don’t know. It may be that a Jew would also deserve the death penalty, and so in principle this is equal treatment for gentile and Jew. Except that a Jew is given some leniency: either because he is obligated in more commandments and bears a greater burden, and therefore he is forgiven more and given more chances to continue. Or because the continued existence of a Jew has greater importance, since he is obligated in more commandments, and therefore he is not killed quite so easily. By contrast, a gentile who does not fulfill his obligations has no justification or value in his continued existence, and therefore is liable to death. Or perhaps a gentile requires immediate deterrence, otherwise he will not fulfill his obligations, whereas a Jew may fulfill them simply because the Holy One, blessed be He, commanded him to do so (see the midrash that the Holy One, blessed be He, went around to all the nations offering them the Torah, and only Israel accepted the command itself. The gentiles asked what was written in it—that is, from their perspective, the mere fact that there is a command was not enough to obligate them).