While amusing, the premise is flawed. 0xF5 is pronounced "two hundred forty-five". Of course, just as with decimal-expressed numbers (e.g. phone numbers), it may sometimes be useful to list the digits; our existing digit names should be sufficient but could certainly be improved for distinctiveness.
But we can think of the words "two hundred forty-five" as meaning `2 * radix^2 + 4 * radix + 5`. We implicitly assume `radix` is ten in spoken English, but the implication in the clip (and the premise of the article) is that radix=16, and the implications of that are followed. There's no reason why the meaning couldn't be inferred from context.
If we were being pedantic, we'd need to come up with new words for every place value, which is way more impractical, and way less funny.