It's a joke. It's a made-up word, a combination of the two words "air" and "Armageddon."
"Armageddon" is a place name from the Bible. It is the name and spelling used in the classic 1611 English translation known as the "King James version." It is the place now known as Megiddo. In the New Testament (the second half of the Bible, specific to Christians) it appears in the Book of Revelation. This is the last chapter of the Bible, and describes the "end times," the things that will occur at the end of the world. The passage is Revelation 16:12-14, "...to gather them to the battle of that great day of God Almighty.... And he gathered them together into a place called in the Hebrew tongue Armageddon." So "Armageddon" is the final great battle between Good and Evil.
By extension, "Armageddon" has come to mean any gigantic battle. It suggests a colossal, grand, epic struggle taking place in the future. For example, someone might talk about a "nuclear Armageddon," meaning a final nuclear war that might end human life on earth.
Here, it is being used in a lighthearted or joking way. It is a televised program of a contest between teams of children flying drones. So, it is a colossal battle, "Armageddon," being fought in the air, hence "Airmageddon."