They were both experienced well trained pilots flying for a good company.
Ok just after rotation at slow speed they may have not contained an engine failure but this was two miles further on.
The temperatures were low, there were no PAX so depending on fuel loading probably light.
There is no reason that aircraft should not have performed well engine out which would have caused them to be flying level low.
So unless the good engine was shut down by accident it doesn't make sense for engine failure
Pace