I don't like being pedantic about language but given that the word is literally just a portmanteau of electricity and execution it's stupid to use it to refer to something other than death. It's not like execution can refer to someone being hurt. The only reason to use it to describe something nonlethal is because you don't realize that execution is part of the word.
Besides, "electrocuted" is a useful word and much less cumbersome than "killed via electrocution". We already have shock, arc, flash and burn for injuries and no other word to clarify lethality.