He was absolutely serious. That said, he was a bit flip-floppy, at first saying, “Absolutely,” then saying, “No,” then saying, “It’s going to happen anyway.” Keep in mind, this wasn’t normal political flip-flopping: it was all in the same interview, within just a few minutes.
He was clearer on the matter of Japan and South Korea having nuclear weapons. With Saudi Arabia, his overall attitude seemed to be, “They’re going to have nuclear weapons, so sure.”
We can quibble over the use of the word “should” in Hillary’s speech. He definitely said that Japan and South Korea should have nuclear weapons. He then added Saudi Arabia to the list, only to equivocate a bit. Still, it’s pretty clear Trump has no intention of stopping Saudi Arabia from getting nukes.
Here’s the video: https://youtu.be/ARIIonzffMw?t=17
Starts with a couple seconds of context, then it goes straight to Donald Trump talking w/ Anderson about nukes.