Yes, some dictionaries include injury, though it would generally be used in the industry (which I worked in before) to describe death ( and it comes from the word 'execute') or maybe sometimes when someone experienced a serious, near death injury, like they got frazzled -- not just a small shock.
Electrocuted is a very strong word and usually used to describe death (or near death perhaps)
Otherwise, what's the difference between electrocuted and electric shock? Death is usually the difference, or maybe some life-altering, serious, grievous injury.
I've had numerous electric shocks. I've never been electrocuted.
I didn't know there were 5 dictionaries that actually mattered. I checked Cambridge. It just said "death." I didn't see it mention injury, but know others do, such as Oxford.
Okay, if you are saying they got electrocuted. What injury did they sustain to make you say that? They felt the electricity isn't enough.
I feel as though you would render the the phrase 'electric shock' obsolete, cos apparently even the slightest shock is enough for you to say electrocuted.
It is a very strong word.