Key word here is "cannot be elected more than twice". So as long as there is no official election, he is not technically violating the constitution by remaining in power. I'm playing devil's advocate here.
That said, I don't think it matters at all. This isn't a Trump problem. Sure, he's the figurehead, but there are ample figureheads waiting in the wings, just as malleable to the alt-reich's needs. They will be more than happy to step in and allow the current dismantling of the USA to continue, and for Something Very Else to be built in its place.