Would calling for the seizure of guns from unnamed citizens and the suspension of due process in doing so constitute treason?
Treason is basically the only crime explicitly defined by the Constitution. According to Article III, Section 3:
Treason against the United States, shall consist only in levying war against them, or in adhering to their enemies, giving them aid and comfort.
So, no. What this hypothetical president is calling for is unconstitutional, is almost certainly grounds for impeachment, and may even be criminal, but treason it ain't.
And that's assuming he actually does it. Simply calling for it, without acting (or directing others to act) to bring it about, may well be protected by the First Amendment.