It doesn't minimize the game, but when the cursor leaves the active portion of the game window, the parry button freezes in place. Ren'Py is then slow to register when the cursor re-enters the window, leading to at least a quarter second delay before you can continue shaking the button, which is damning when you have such a short time to perform the mechanic.
I ended up having to disable my other monitors in order to finish the mission.
Yes, specifically it's 21:9, so when playing a 16:9 game there's always a lot of blacked out screen space.
Fullscreen isn't really part of the issue. If anything it slightly helps, because it slightly reduces the amount of unused space.
I normally play just maximized, but had to turn on fullscreen for this just to get that little bit of extra active render area.