Does "encounter" here mean he does this once PER encounter, or that it lasts for the DURATION of the encounter? The latter makes more sense.
Also -- given the idea that feats are 'built into' monsters, how do we figure out what happens if the barbarian loses his axe and has to grab a sword? It guess we can reverse engineer BAB (/12 level) +str bonus, and assume the difference is a 'built in' pseudo feat. Lessee, it's level 3, so that's a +1 BAB, Str is +4, so total attack bonus should be +5, his actual bonus is +6, which would be the equivalent of WF(Greataxe). Unless his BAB is +2 -- where does the rounding occur? -- which makes the handaxe make sense, unless he also has WF with THAT, which is not impossible.