Here is another odd thing...
It is odd. The rest of this assumes Windhoek's version is the truth.
Questions - what was he doing when Imprey burst into the room?
He'd been cooling his heels waiting for the Princes to finish their "discussion". Imprey arrived and waited with him until the live feed from the Throne Room meant Imprey had to burst into the room regardless.
Dulinor's arrival in the Throne is the signal to the rest of the plotters in the Palace to begin the previously planned
overt actions. Up until then, their actions had been covert. The Palace's own news feed system signaled everyone when to start.
Why didn't Imprey consider Windhook a threat?
Windhoek isn't armed and isn't a bodyguard. Imprey probably marked him for a bullet, but the guard and the Princes were his primary targets.
Why didn't Windhook attack the assassin from behind?
First, he isn't a bodyguard and wouldn't react that quickly. The fact that Imprey muttered something like
"It's time..." and entered the Princes' quarters without permission would have stunned Windhoek.
Second, he doesn't have a chance because Imprey is killed almost immediately. He bursts in drawing attention to himself, begins firing immediately, and is taken out by the guard just as quickly.
Imprey rushed his end of things by fixating on timing rather than results. Because Dulinor is going to be killing Strephon momentarily, he can no longer wait in the hallway and violates protocol by entering the quarters without permission drawing attention to himself. He then starts shooting immediately instead of coming up with some patter that would let him get closer and get the drop on the guard.
A section from the Ilelish Guards would have got the job done, but maybe Guards in that part of the Palace would have raised eyebrows and maybe Guards couldn't get to that part of the Palace from their usual posts quickly enough to make sure the Princes couldn't escape once the Assassination was broadcast.
It's all poorly planned which makes me wonder if it was something added at the last moment. I wonder if the Princes had been scheduled to be out of the Palace only to change their plans within a week or few days of 132?