Suppose that some rude person said, "Blowing your nose is what you ought to do." This person would not mean, "The property of blowing your nose is the same as the property of being what you ought to do." That claim would be absurd. That person would mean, "Blowing your nose is, or has the different property of being, what you ought to do."
In the same way, "maximizing happiness is what we ought to do" means "maximizing happiness is, or has the different property of being, what we ought to do."
But there's an important disanalogy here. The utilitarian claims that maximizing happiness exhaustively specifies what we ought to do (i.e. in every situation). Parfit's imagined rude person is presumably making a very different sort of claim. He merely claims that blowing your nose is what you ought to do in this case. If he were making the same sort of claim as the utilitarian -- if he were claiming that an act is right just in case it is an act of nose-blowing -- that would indeed be "absurd". But it would be an absurd normative claim. It is less obvious that there is any additional absurdity in moving from this normative claim to the meta-ethical claim Parfit wishes to deride, i.e. that the coextensive properties are thereby identical.
So, while I agree with Parfit's conclusion, I don't think this particular example provides much support for it. The two cases aren't functioning "in the same way" at all. The rude person is very obviously using the 'is' of predication, in merely talking about a particular instance of 'what we ought to do'. The (e.g. utilitarian) normative theorist makes much more expansive claims about 'what we ought to do' (not just here and now, but in all cases), which at least opens the possibility that they are using the 'is' of identity.