Further, even if you can define the concepts of "omnipotent" and "omniscient" is self-consistent ways, the existence of those qualities as anything but abstractions, as qualities that must be manifest, is highly debatable.
It's one thing to imagine, for example, "the world's fastest runner". Define a particular metric for running speed and everyone who runs will have some rank by that metric, at least hypothetically. There's got to be one person who ranks higher than everyone else (or perhaps a few in a tie for first place). For whatever scale you can imagine, if that scale measures a real and clearly definable thing, there will be a top to that scale, and at least one embodiment of that top ranking value.
I think the appeal of this particular theological argument is supposed to be that on the scale of "greatness", there has to be something that is greatest, and that greatest thing would be God.
As soon as you involve properties like "omnipotence" and "omniscience", however, you've broken that paradigm, as if you're no longer talking about "the world's fastest runner", but "the runner who can run a mile in 0.2 seconds" -- an entity very unlikely to exist, certainly without any foreordained necessity of existence.
The cited text states that the argument is not convincing, which I believe fits with what the column is arguing.
The article is also trying to make the case that there are more sophisticated arguments for God that atheists aren't typically prepared to handle. If this "modal-logic formulation" is supposed to be an example of something that would stump a person like Richard Dawkins, I'm not impressed.