Agape = unconditional love
That definition is more theological than linguistic, I'm afraid.
The JW claim, (which I heard a gazillion times as a teenager) was that ἀγάπη was a "principled love", as in a higher, more pure form of the emotion.
The word actually means love as a general principle, which can be used in any number of ways.
Pederasty, for example, was common in Ancient Greece and ἀγάπη was the word used to describe affection within those relationships.
So maybe it's better that the JW's no longer frame entire arguments around preferential definitions.