A pile of gunpowder that is lit will just burst into flame. BUT... if you put it inside layers of paper and then ignite it... BOOM. I suspect this is what happens with e-cigs. The battery ignites, but is sealed inside the plastic cartridge of the 'pen'. The expanding gas can't go anywhere until it bursts the plastic open.
BOOM !!!!!
But, that is NOT what is described here. The majority of the boy’s physical damage is internal, to his mandible, his jaw, with minor damage to his lips on the outside, from a battery "explosion" that had to have occurred in his hand, several inches away from his mouth, with his lips between his mandible and the battery. The plastic is weak. There are many parts between it and him. You could actually have a small caliber bullet explode at that distance from you with little damage because it’s uncontained. You’ll get burns, but not much damage.
The damage to his mandible, "equivalent to that from a car accident" does not comport with the power available in a Lithium Ion battery at that distance. Something smells.
Another possibility is that he tripped and fell, driving the e-cigarette into his mandible at the impact point. That could account for the damage I see, but not any explosion. A fall would account for any shattered e-cig.
Now a home made one? You could literally make a pipe bomb.
I think that's it. The e-cigarrette acted like a primitive "cannon" with the exploding battery propelling pieces of the cigarette holder into the kid's mouth.