Does throwing Krieg the Psycho's axe when Buzz Axe Rampaging count as melee?
yes it does... you'll notice when speccing into skills like "Silence the Voices" a thrown axe does the same amount of damage as a melee swing.
Buzz axe always deals 60% of the melee damage. That's just the cost of it being ranged. If it wouldn't be lower it would be considered op since you could oneshot enemies at extreme range if you could aim properly.