Secondly, this argument assumes that order has to be designed, and can't just occur naturally. But the way things happen to be will give them some characteristic features, which may appear as order. Very often, patterns follow from the nature of the thing in question. We know that a spider doesn't have a planning intelligence - the pattern of its web has arisen through millions of years of evolution by natural selection. Ironically, followers of Aristotle's kind of god have often been condemned as secret atheists by Christian leaders.
Ontology is the study of the philosophy of being.
To be honest, I just don't see how these extreme philosophical arguments can tie up with reality. This argument comes from St Anselm in the 11th century. Later, Descartes revived it, and it has been taught ever since. It's the sort of argument that will convince those who desperately want to be convinced. But existence is not even an attribute in philosophical terms.