This sentence was an example sentence in a section of "Du's Handbook" that said "其 (기)" was sometimes used to indicate supposition, especially about the future. "Du's Handbook" seems to have translated it as "would, I think," a translation I can understand. However, how did the Handbook translate "於 (어)"? They seem to have omitted it. Therefore, I would like to suggest the following translation:通於此說者, 其知所以爲天下乎“One who understands this theory would, I think, know how to rule the Empire.”
According to my Korean dictionary, 於 (어) can be used not only as a preposition, but also with the meaning of the verb "따르다," which means "to follow." Since a preposition seems out of place in this context, I assumed 於 was being used with its meaning "to follow." Therefore, "通於此說者 (통어차설자)" literally translates as "know (通) [and] follow (於) this (此) theory (說) person (者)."通於此說者, 其知所以爲天下乎One who knows and follows this theory (通於此說者) probably (其) knows (知) that by which (所以) to rule (爲) the empire (天下), yes or no (乎)?
My Korean dictionary also says that one of the meanings of 爲 (위) is "다스리다," which means "to rule over."