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.
>>apprec+(OP)
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’.