Just as the definition of a circle makes it impossible for it to be square, so the definition of God makes it impossible for him (her, it) to be non-existent. In both cases we are talking about the way the language-game works.
There is no doubt that we find the language-game for a circle very useful for discussing all sorts of patterns in existing and non-existing things. We can hardly imagine the language of geometry without it. Similarly, whether we are atheists or theists, we can hardly imagine discussing God without an agreed language-game for the word.
But as Donald F. Henze pointed out, no rule of a language-game can be logically tied to words, entities, or activities outside the language-game. It cannot bridge the gap between the language game and whatever lies beyond it. ("Language-Games and the Ontological Argument," Religious Studies, October 1968).
The Ontological argument is therefore a very useful statement about the language game for our use of the word God. In that language-game God necessarily has to exist. But it does not get us very far in clarifying the language-game we need to make sense of the Bible.
For a start, the language-game for the word God in Genesis 1 is Theistic : God is viewed as the Artist of our world. But the Ontological argument would apply equally to Hindu Monism. In Modified Monism for example God is the soul (animating principle) of our world, and in that language-game it is impossible for God not to exist. In Pantheism all that there is is God, and in that language-game God's eternal existence is also a necessary part of what is meant by the term.
But then we need a further clarification of what we mean by God in Trinitarian
Theism. God is necessarily an eternally existing family oneness of three
Persons united by love. Trinitarian Christians cannot do without that language-game
anymore than geometers can do without a circle. And I cannot think of a
greater perfection than the love of God. But that is not a logical proof
for the existence of God, only an explanation of how we want to use the
term.