Per the Constitution, the US government is comprised of 3 co-equal branches. The Executive Branch is only one branch, not the government itself, so technically its taking over of the entire government could be looked at as a coup. So far the other two branches are either cooperating (legislative) or sitting idly by (judicial), so we don't know yet whether this is a coup by the executive or just the entire government saying fuck the Constitution, we're done with that.

You could also say, since this is supposed to be a government of the people, by the people, and for the people, that it is a coup against the people--but the problem there is that, assuming the election wasn't interfered with, "the people" elected this government.