In the previous post I mentioned R' Shteinman's question as to why Pharoah should have been obligated to listen to Moshe -- the commandment to listen to a Navi is among the 613 mitzvos we are bound by, but not one of the 7 mitzvos bnei noach. R' Shteinman suggested that since it was obvious that Moshe was acting as the messenger of Hashem, Pharoah should have listened. In other words, as a comment put it, this is an extension of the basic mitzvah of emunah.
It occurred to me that one could answer the question based on an idea R' Elchanan elaborates on in Kuntres Divrei Sofrim which we discussed a few times in the past (see here). R' Elchanan suggested that the ratzon Hashem is its own mechayeiv -- that is, knowing what G-d wants, even if one is not explicitly commanded to act on that knowledge, demands a response. Bilam was punished for following the messenger's of Balak because he knew that G-d did not want him to curse the Jewish people, regardless of whether there was a formal command for him to desist from going. The Ramban maintains that we are bound to follow dinim derabbanan not because (as the Rambam writes) there is a command of "lo tasur", but simply because a din derabbanan is an expression of G-d's will. Here too in our case, it is not because a formal mitzvah to listen to a navi which obligated Pharoah to obey Moshe, but rather because Pharoah should have understood that Moshe's direction was the ratzon Hashem.