The Ramban there in Shmos 12:16 asks a similar question to yours. He asks: if "acheirim" in Rashi refers to Jews, they are anyways forbidden to do melacha. If it refers to non-Jews, the Gemorra in numerous places in Shabbos is explicit that there is no issur d'oraisa. He concludes that the derasha Rashi is quoting from the Mechilta must be an asmachta.
The halachos of a Shabbos goy are very complicated, but suffice it to say that while there is no issur d'oraisa, many people frequently transgress the issur d'rabannan.