The Oxygen Destroyer didn't kill Godzilla movie, the Oxygen Destroyer was a lethal weapon designed by scientists to kill Godzilla. Designed to split oxygen atoms, the Oxygen Destroyer kills anything it comes in with. In the first movie, it successfully killed Godzilla, solidifying its place as one of the most important plot devices in Godzilla franchise, and it's been referenced numerous times since.
Given its significance, it made sense for Legendary's MonsterVerse to do their own version of the Oxygen Destroyer. During Godzilla's second battle with King Ghidorah, the military arrives on the scene, with iral Stenz (David Strathairn) announcing their intent to take out both monsters with the launch of their new weapon, the Oxygen Destroyer. He expresses confidence that no creature can survive the blast from the Oxygen Destroyer. After it's deployed, Godzilla is critically injured and presumed dead. But their plan backfires when King Ghidorah flies out of the ocean, wounded from his fight with Godzilla but seemingly unaffected by the Oxygen Destroyer.
true King of the Monsters could not? The explanation for this is likely related to a discovery that Monarch makes about Ghidorah shortly after his fight with Godzilla. The main characters are able to figure out that Ghidorah isn't from Earth. Much like the Toho version of the three-headed monster, the MonsterVerse's Ghidorah is an alien invader from another planet. Ghidorah traveled to Earth from space centuries ago, and he's been here ever since.
The military knew they could defeat Godzilla with the Oxygen Destroyer, but they didn't count on Ghidorah being unaffected. This could be because they assumed that Ghidorah's body functioned just like any other living creature from Earth. Naturally, it would be believed that Ghidorah requires oxygen to survive, but Ghidorah is an alien. With that in mind, there's no reason to believe that the Oxygen Destroyer should kill him. No one completely understands his biology yet.
Ghidorah not needing oxygen to live would explain how he reached Earth in the first place. In Toho's movies, Ghidorah can fly around in space without a spaceship to carry him, so unless he was transported by an alien vessel, Ghidorah must have come to Earth on his own means. If Ghidorah doesn't need oxygen to survive, then there may be nothing stopping him from freely flying around space. Ghidorah being able to survive the Oxygen Destroyer because he's an alien is one more way that the MonsterVerse's decision to keep Ghidorah's Toho origin has added a bit of a fun, unpredictable factor to the classic Godzilla villain. Ghidorah's nature as an outsider is the reason why he defied the natural order and became such an enormous threat to the planet.
