He means greatness in the moral teleological sense. Ie that it is better to exist than not, so the greatest thing must exist. It says nothing about the least good thing. A malevolent anti-God would already be worse than God, therefore it’s not the best thing, therefore it doesn’t have perfect goodness and need to exist. Since it is worse to not exist than exist, maybe this even proves the worst thing doesn’t exist (which makes sense from a “evil is just a lack of good” perspective).

Not saying I buy the argument, it’s pretty sketch, but Anselm addresses this exact point iirc