Maybe when it says Akum Sheshavas it literally means an Oved Avoda Zara. In that case he is not being Shoves to show that Hashem created the world and it might even be an extension to his own Avoda Zara.
Another possibility is the opposite of what you quoted earlier. He is Mechuyav to rest enough to show a Shvisa, that Lechvod Shamayim he is not working. But this has nothing to do with the 39 Melachos necessarily.
This can actually answer Tosafos’ Kasha in that it is an Assay and not like the rest of the 7 Mitzvos Bnei Noach.