Well.... you are making a ranged weapon attack with it when you throw it, so you could argue that the first two bullet points apply. (Using the same logic that allows a hand crossbow to count as a "one handed weapon" when using the Crossbow Expert feat. i.e. The axe is a weapon and you are making a ranged attack with it. )

The -5/+10 bit wouldn't apply, as that specifically requires a ranged weapon.

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