If he's short vol., then he doesn't need to delta-hedge unless he's also directional. But then if he's short vol. AND directional then it's not a butterfly. LOL You cannot be all three at the same time, non-directional and short vol. and be butterfly. It just does not make sense.
And the strategy is not very profitable unless you trade huge volume cuz you are basically limiting yourself in movement and the magnitude of it. In order to make $$ in options, you have to be correct in predicting 2 things, 1) the direction of the move and 2) the magnitude of the move. The $$ comes in with the risk on one or both of them. His strategy wants to reduce or eliminate risk in both then his profit is going to be reduced or eliminated as well since in an efficient market, there is no or very little risk-unadjusted returns. And even if you have large trading capital, this strategy is not very capital or cost-efficient and it's certainly not suitable small trading accounts. The profit will be minuscule with huge commissions. You will be much better off just trading the underlying and hedge.