To the best of my knowledge, the position being advanced in defense of Congress not being able to compel those two figures to testify is on grounds which the courts have never considered directly before. It is different from the Nixon precedents you're thinking of (which were about compelling the White House to hand over taped recordings of conversations).
One possible source of confusion is that the closest precedents here arise from another, completely different and much later case where Nixon was a party, one from 1982 where he was being sued in civil court for actions he ordered as President. The claim being made then (and here) is that the President has an "absolute immunity" from being compelled to provide testimony about their actions as POTUS. In 1982, SCOTUS ruled the President did have an absolute immunity against being compelled to provide testimony in civil court about their actions as President. The question of whether the same immunity applies to testifying before Congress has not been addressed (one could argue either way, particularly wrt impeachment proceedings). A related ruling to that one addressed the topic of whether that absolute immunity applied to the President's closest/senior advisors. SCOTUS ruled against that claim then.
Again, whether that applies to testimony before Congress has not been addressed but if stare decisis were being followed it is rather unlikely to go the White House's way here wrt the advisors. It is, however, entirely possible that the courts will just punt it as nonjusticiable and say "this is really something Congress and the White House should be working out themselves via the negotiation and accommodation process, not a matter for the courts at this time." Dragging the courts into it is also in all likelihood a delaying tactic. The cases can easily take longer to work their way through the court system than Pelosi et al are willing to let the impeachment proceedings themselves take to finish. In which case the cases will get kicked because there is no longer an active question (and hence justiciable controversy) before the court and those plaintiffs will have managed to skin out of testifying.
Someone does not have to show up to claim Executive Privilege. In fact, EP is usually claimed on their behalf by the White House. You do have to show up to plead the 5th, but that's a very different matter legally speaking.