Better to loose the motor than the boat. With it hanging there swinging in the waves, it could have damaged the other motor at any time, and a boat with no propulsion beam on to the waves is at high risk of capsize - all it takes is ONE breaking wave higher than the beam width and it can flip you. Slinging the outboard to the side under the stern isn't an option in that sea state - its not a sailboat so doesn't have the winches to get it there, they didn't have enough crew to manhandle it, the risk of serious injury getting a line round the foot or leg is unacceptably high, the risk of hull damage is far too high, and the boat would have been virtually uncontrollable with that much drag under the stern on the opposite side to the remaining propulsion.
OTOH in that area the ten fathom line runs a mile or two out from the coast, so once the steering linkage was
cut detached* and the immediate danger was reduced, I'd have tried to hitch a very long line to the umbilical before cutting it, lead outside the guard rail, and up to the engine, so it doesn't foul when the motor drops with a fender or any other convenient float on the other end. Maybe they just didn't have a long enough line quickly accessible, or maybe they just didn't want the additional risk with a child on board.
They did recover the motor, by diving on the GPS waypoint, in 100' of water:
https://youtu.be/rbzk42XW4ikand Alfred Montaner rebuilt it:
https://www.youtube.com/playlist?list=PLilx-dswyaa5LRTaHt6jv5Em9P8Im8Q4z* Power-boaters are a different breed - any experienced yachtie would have had heavy duty bolt cutters, and a long heaving line, often with floatation on the end of it, stowed where they could be grabbed in seconds.