... you have to consider the context. I see your point about ... 1 sufficient, but within the context of the statement, it isn ... will need to consider the context before blindly diagramming the statement ...
Similarly, "not both" can be used in a way that be applied to just about any type of game whether it be sequencing or grouping in nature, so context is very important.
The first sentence is just context and does not have a place in our conditional chain. You are correct that the quantifier ELCI should "some" over to LCI. So replace ELCI --> LCI with ELCI -some-> LCI. Still ac(A) is correct. Nice spot!