"create a monument to non-existence" is the memorably odd threat that the villain Kefka threatens the party with at the end of Final Fantasy VI.
Final Fantasy VI was considered at the time of its release one of the most sophisticated RPGs, eschewing the standard swords, sorcery and lost princesses for a game about technology, the environment, and the corruptions of imperialism. Although the sophistication and convultions of the themes were still degrees below Final Fantasy VII, it was a very complex game for its time. Kefka's place in the game is not altogether clear, however. He seems to be a standard caricature of a villain, sometimes played to the heights of parody. He is amoral and more famous for his cackling laugh than for his motivations in trying to rule the world.
So this line, one of the last of the games, presents an interesting dillemma. Does Kefka have some sort of philosophical belief in nihilism that is driving his destruction, is he merely insane, or did the game's translators (many people think that this game was translated poorly) put this in as a melodramatic line out of lack of any other ideas.
In any case, there is the additional question of what a "monument to non-existence" would look like, and whether the term itself isn't an oxymoron.