He is assuming that there will be a doomsday - also known as begging the question

No, I don't think so. He is making a claim about what implications follow from a certain fact. That fact is the definition of "a doomsday prediction". All that follows from that definition is that all but one will be false. Of course, even that last one (so to speak) might be false, but, even if this is so, it doesn't follow from the definition.

This is not a case of begging the question. It is just being clear about what implies what.