All planes are definitely capable of taking off safely even if they lose an engine at the worst time. Whatever happened here, I would be shocked if lack of thrust in the 2 remaining engines was a significant factor unless someone really screwed up the load calculations and they were overweight for conditions.

Single engine planes (GA, and some military planes) don’t handle this condition well at all.

In fact, for awhile (maybe still the case), the #1 killer of skydivers was single engine failure on takeoff from the jump plane (and similar aircraft failures), not accidents ‘while skydiving’.

Lack of thrust in the "taken out by debris" sense seems to be the case here.