First, it should be noted that this game engine does not possess (a) mechanical lever/widget (like an essential piece of PC build that richly encodes novel theme or gives specific expression to motivation which constrains the GMs content generation accordingly while simultaneously rewarding you for pursuing your player-authored themes/motivations) nor (b) a procedure-based vehicle for players to flag theme/motivation/relations that the GM should be challenging during play (like a Session Zero or a principle of 'ask questions and use the answers"). That is a crucial piece.
Now lets take a look:
* "If you want to get the PCs involved in whatever you (the GM) have designed for them to do"...<give them...motivation...and they will do what you want them to do>
You've got that backwards. What you posted isn't about giving them motivation to do something. It's about testing the motivations that the PCs gave to themselves.
The first example tests the player established motivation of greed. Will they risk their lives to overthrow an evil powerful enough to threaten an entire kingdom for mere gold? Or will they refuse and go somewhere else?
The second example tests the player established motivation of dedication to their comrade. Will they risk their own lives to see that dedication through, knowing that they are weak(wererats are a threat and gargoyles killed one of them)? Or will they give up the quest and bury Mialee, giving her a beautiful funeral with lots of flowers?
The third example tests the player established motivation of self-preservation. Will they preserve their existence by removing the powerful vampire threat? Or will they preserve their existence another way, say by fleeing far to the south where the vampire will never find them?
The fourth example tests the player established motivation(s) of loyalty to family and/or the PC established motivation to help those in dire need. Will they risk their lives, possibly for free(also testing the greed motivation) to help something that has threatened an entire dwarven city? Or will they turn it down?
The text you show incorrectly says that the DM is tailoring motivations. He is not. In every example the DM is simply tailoring tests of those motivations that the DM already knows the players have established for their PCs.
* Then, this section on Motivation (which might have been a section that actually gives rise to player protagonism in which the players' rich themes and motivation actually give rise to the shape and trajectories of play) goes on to talk about how the "tailored motivations are ones that you (the GM) have specifically designed" (you are giving the players the motivations to engage with your content...the players aren't giving you, the GM, their own motivations to generate particular content). Lets look at those bullet points:
1) No attachment mercenaries interested in gold!
2) Fetch Quest!
3) Deus Ex Machina of the content they just resolved!
4) This one gets the closest to possibly engaging an actual player motivation that is generated by a player but we surely don't know (and given the above text, why would we suddenly interpret an inversion of paradigm?). Note that they don't (a) put Tordek's brother specifically at stake, (b) we have no idea if this is a consequential NPC that the player brought into play and made actual connections with (but we definitely know there is no system tech/PC build tech facilitating this because the game doesn't have it) or just NPC001 generically skinned as kin and giving a Fetch Quest (see 2), and (c) note they didn't say "Hometown"...so how do we know Dumadan isn't just DWARFCITY001 because dwarfey-trope where if the player doesn't jump at it they'll get metagame derision for "you're not playing your dwarf right!" Social pressure to play their character the right way is definitely not "control!"
It really is a section on player protagonism. It's not very strongly written, and says it's the opposite of that, but all four examples test player established motivations.
It's poorly written, but if the DM follows those examples and tests things that he knows motivates the PCs, player protagonism is established. This happens even if the DM is trying to get them to do what he wants. How? Because the section is about him creating those tests as the thing that he wants to happen.
The DM can't control the outcome of those tests of player established motivation. The section doesn't talk about forcing them to undertake saving the kingdom out of greed. Nor does it say to keep coming up with test after test after test until they conform to what he wants. It only talks about testing the player established motivations as incentive for them to do something.
GM has exclusive authorship over all content (from situation to setting to main plot to auxiliary content and even authoring PC motivation to facilitate engagement with their prep…and then they have a massive roll in action resolution mediation on top of this) of consequence and the result is overwhelming control over the shape and trajectory of play.
NO! At no point in any example has the DM authored ANY motivation for the PCs. He is authoring tests of motivations that the players have established. They are already motivated by gold. They are already motivated to bring their companion back. They are already motivated by self-preservation. They are already motivated by family and/or compassion. The DM established none of the motivations in the examples.
As I said above, what it tells the DM to do, "Tailored motivations..." is at odds with every example given, "Tests of player established motivations." The designers essentially misspoke and really meant "Tailored tests of motivation."