TBH, I was thinking on a reply on my way home, but decided to check the video first. To my surprise, it had my answer right there: namely "failure is a consequence".
Since we were just talking about (fake) urgency, I guess the most common "motivation" for the player is the looming catastrophe. But letting it actually happen would amount to a failure state. And a lot of games don't want players to fail.
Even on a small scale, there is often no opportunity to make a wrong decision. No wrong answer in dialogue, no way to irreversibly fail at the solution of a puzzle, no dungeon area that remains forever locked if we do or fail to do something.
How can there be real urgency if nothing negative or inconvenient is allowed to befall the player, no matter the scale?
That's called "bad design" and "hand-holding consolitis". I.e. BiowEAre. Of course failure is a consequence. In Planescape Torment you could fail conversations let alone anything else. Failure should be a consequence not because of "hurr durr console tards don't know challenge" but out of the overarching goal of creating a believable world with real causality. Failure also doesn't mean the "game over" screen, though that is one state of failure.
And the "game over" screen is probably the worst way to implement failure. Certainly a necessary evil in many games, but I much prefer less binary fail-states. And also subjective fail states. Say you have to defend a village from monsters, and there's lots of villagers that can be killed. The likely fail state probably won't be you getting killed, but the village being decimated. A way to signify that the player has done a more or less crappy job defending if more than X% of the villagers have died can be a good way to create a non-binary, subjective fail state. Some players won't care if a bunch of people die, and may just use them as meatshields. Or you might even prefer they die if, for some reason, their essence is being used to power some sort of artifact, and the more of them that die, the stronger the item.
As for urgency, I would really like to see, for example, the magisters show up on the island eventually, but you either need to have some way to show that time is passing to the player, or their arrival needs to be tied to certain events (the much more likely and easier solution.) It could be tied to one main event, or maybe if you complete 5 side quests, a party has arrived. I think this would work much better for something where people are trickling in, like refugees or a disorganized monster invasion, instead of for a ship, where the arrival of a big group of people is fairly binary.