True. It should be noted, though, that the compact will have no effect in states where the majority of people voted for the national popular-vote winner. It would only have meaningful effect in states where a majority of people voted for the other candidate. And in that case, the message would be that "We don't care who the people in our state want for President--we want to let other states elect the President."
Indeed, viewed from that perspective, it would seem questionable whether such a compact violates the requirements that states have a republican form of government.
More accurately, where a majority of people voted for any other candidate. It's overwhelmingly likely to be the "other" major-party candidate, since no third-party candidate has carried a state since 1968.
That's a pretty interesting argument. If enough states signed on, you could have a decent argument that states that belonged to the compact and whose voters opted for the losing candidate effectively didn't have their votes counted at all. That could be challenged on one person, one vote grounds, or under equal protection. But it would be difficult for SCOTUS or Congress to use that kind of argument to overcome the basic fact of states' power to allocate their own electors.
"And in that case, the message would be that "We don't care who the people in our state want for President--we want to let other states elect the President."
Absent a specific constitutional prohibition, the state's representatives, provided that they were duly and fairly elected, are empowered to make that call. Whether it's the statewide vote, the national vote, or the pick of the tic-tac-toe playing chicken at the county fair. If the voters don't like it, they can elect people to change it. Democracy only guarantees the people's choice, not the smart choice.
Indeed, viewed from that perspective, it would seem questionable whether such a compact violates the requirements that states have a republican form of government.
On what grounds? Unless there was force or fraud, the candidates were duly elected, and the voters had the opportunity to revisit their decision every other year, at least. Anything the government does, another slate of candidates can undo. Something doesn't become undemocratic or unrepublican because you disagree.