As a side note, at 30 degrees AoA the aircraft will not be able to continue flying anyway, the wings will have stalled well before that, and the pilot would be made painfully aware of this fact through stick shakers, aural warnings, and very rough tail buffet.
I'm a flight test engineer, so this stuff is what I get to do for work! :)
[1] https://petapixel.com/2016/01/25/this-dramatic-shot-was-done...
(Unintentionally reduced spoilers due to having forgotten many details of the film.)
Look again at the actors. Smiley never stops studying the others' face, while the other looks scared, nervous, shifty, and guilty the entire time. Even without context you should be able to pick up that Smiley is cool as ice, and that the other man has something to hide.
The PLI is capped at 30 degrees pitch, but that does not mean that the plane would stall at 30 degrees. You could climb much steeper than that if you had enough speed:
> However, the PLI also is limited to 30 deg of pitch attitude, regardless of AOA. If AOA or AOA margin to stick shaker were to be used as the first and primary focus of the flight crew during windshear escape or terrain avoidance procedures, extremely high pitch attitudes could be reached before stall warning if the maneuver is entered with sufficient speed. Therefore, the PLI shows the lesser of either margin to stick shaker, or 30 deg of pitch. (http://www.boeing.com/commercial/aeromagazine/aero_12/attack...)
Nevertheless, at least according to some Wired article, one of these steep takeoffs was done at a little under 30 degrees. (https://www.wired.com/2014/07/watch-test-pilots-push-the-new...) I guess the pilots use the PLI to judge their pitch attitude.
Boeing also released a video of the pilots rehearsing the routine. There's an overhead view of the takeoff - that's a lot steeper than 30 degrees, unless it's a perspective trick.
EDIT: 50-55 degrees seems to the actual pitch angle.
As long are you have enough thrust, airspeed and no system preventing you to go above a certain pitch or AOA, then the plane should fly just fine...