Harris' issue there is that he doesn't understand the is/ought gap. He seems to think it's the thesis that there cannot be moral facts, when it's just the idea that any argument for a normative conclusion must contain a normative premise (i.e., that the conclusion must follow from its premises). And his own take on moral philosophy actually does bridge this gap, since it goes roughly like this:

1. If our intuitions clearly indicate that some moral principle is true, then it is true.
2. Our intuitions clearly indicate that we ought to maximize the well-being of conscious creatures.
3. Therefore, we ought to maximize the well-being of conscious creatures.

That he doesn't acknowledge this might be continuing ignorance, general bloodymindedness, or just the fact that, laid out this way, it's clear that his project is a philosophical rather than "scientific" one as he purports. In any case, the actual problem with his moral philosophy isn't is/ought. It's that he doesn't argue for either premise well, nor even really explain sufficiently what "maximizing the well-being of conscious creatures" means.