Yes, it's the right thing to do. Your shoulders should be retracted at the end of a deadlift rep.
Those videos have the answer. The deadlift is not finished until you achieve full (but not over-) extension, and that includes thoracic extension. "You can't cheat the [deadlift] by leaving your shoulders forward" is exactly correct.
I don't agree that ...
The 2019 IPF Technical Rules Book includes these items which will lead to your deadlift being disqualified in a competition (see Page 9 of this PDF):
"Failure to lock the knees straight at the completion of the lift."
"Failure to stand erect with the shoulders back."
You describe a severe amount of agony in ending the deadlift with your ...