Feif Un,
A beautiful explanation.
I think, though, that it fits better with the first p’shat which HaleiVi quoted from Rash”i, and he was looking to understand the second one.
The explanation of the second p’shat, may I suggest, is that all mitzvos bein adam lamakom also include an aspect of bein adam lachaveiro, because kol Yisroel areivim zeh lozeh, so one person’s aveira affects the next person as well.