But the many worlds view asserts that there are parallel universes, one for each possibility. The multi-universe idea is a subset of this idea. But it goes further.
—Wrong. The multi-universe he describes is completely independent of the many-worlds interpretation of QM. One is not a subset of the other - they have nothing to do with each other. Either one could be true and the other wrong, or both could be wrong, or both correct. (In some classification schemes the many-worlds interpretation is referred to as a lvl 3 multiverse and the idea that there are many universes each with different constants is a lvl 2 multiverse. Lee Smolins theory of fecund universes fits into that category.)
Second, why cosmic inflation is used to support the multiverse notion is not understood by the writer of this article (me).
—Whats being referred to is the chaotic inflation theory, another variant of a lvl 2 multiverse. Basically, pockets of dark energy within a universe producing new universes.
Thirdly, string theory, or the theory that the universe might exist in multiple branes or dimensions, is presently completely unobservable and untestable. However, its advocates would also claim that it is not falsifiable, and therefore, it might be correct. To use this argument is completely circular in its reasoning and short on substance.
—I challenge anyone to find a string theory advocate ever using such an argument.
Short on time, long on interest.
Cheers!