For this to happen, the initiation of the explosive had to take place at one of two points along the center-line of the warhead; at the “fuze” end or 180 degrees out.
From the design of these munitions, I'm betting that somehow, the safe and arm (S&A) device was in-line and for reasons to be determined, the detonator in the explosive chain went off.
The detonator is about the diameter of a pipe cleaner and about 3/8” of an inch long. It can be set off electrically or by a physical mechanical pin strike.
Depending on the design of the explosive train, the detonator generates a shock wave that starts an initiator to explode, which increases the shock wave that sets off a booster (About the size of half the length of a C cell battery.) which sets off the warhead. The initiator is optional depending on the type of explosive and other factors.
All this happens in less than a millisecond or so.
As to why that many Marines were around. Since it was training, I would assume that several gun crews would have been in close proximity to learn and use the equipment.
The 60mm munition is one of the safest known systems. Since it's been a while, I don't know if it is Insensitive Munition (IM) compliant these days or not.
I was never around the 60mm mortar. It seems like there was a safety built in with our 4.2 mortars that the round had to travel a certain distance before it could go off. We had a short round in training ( went like 50 yards) and didn’t detonate. Does the 60mm have this?