His argument here really is exactly the same as an intelligent designer: "magic is too complicated and arbitrary to be the result of some physical process."

He actually does kind of address that, by pointing out that there are only two known processes that produce purposeful effects:

There were only two known causes of purposeful complexity. Natural selection, which produced things like butterflies. And intelligent engineering, which produced things like cars.

Magic didn't seem like something that had self-replicated into existence. Spells were purposefully complicated, but not, like a butterfly, complicated for the purpose of making copies of themselves. Spells were complicated for the purpose of serving their user, like a car.

Some intelligent engineer, then, had created the Source of Magic, and told it to pay attention to a particular DNA marker.

So, yeah, I disagree strongly that the two arguments are "exactly the same". That's the sort of thing you say more for emphasis than for its being true.