In this game:
https://www.warzone.com/MultiPlayer?GameID=34240503

On turn 19:

* Scotty (gray) played an order priority card
* Cj (red) did not play an order priority card
* Cj got the first move

This meant that Cj's army was able to attack my army before it could launch into his territory, futile as that may have ultimately proved.

Do I misunderstand something or did the card not work correctly?

I believe it did not work as I've always understood it and as described in the wiki: https://www.warzone.com/wiki/Order_Priority_Card

oof - nevermind.

Upon review again, after the game was over, I see that he also played a card. There must have been a setting that other players don't see the card play during the game.

yes, "visibility of opponents playing cards: hidden"

Does ABBA apply to Order Priority Card?

Whoever plays most OP cards, gets first move (usually its 1 card for you and 0 cards for opponent).

If both players play the same amount of OP cards, the ABBA move order is respected.