Ok, time for nitpicking again.
The cost of Flying Weapon is 0 Air quanta. This is a duo deck.
0
= 0
= 0
= 0
= 0
= 0
= 0
= 0 anything.
It doesn't matter if you pay with 0 USD, 0 EUR, 0 GBP, or 0 apples, you still paid the same amount : nothing.
There is no difference between paying 0 Air or 0 Aether.
There is no difference between an empty bag that doesn't have any apples in it, and another empty bag that has no bananas in it.
Actually, paying zero of anything, and doing nothing are the same thing as well, but that's a different story.
If the cost determined the element of the card, then Anime Weapon wouldn't have one and would be an "other" card.
This isn't true because it is listed under Air in your deck editor screen, so we can conclude that in elements, the element of a card is not determined by the cost to play it, but instead by how the card frame looks like/ where the card appears in the bazaar.
More importantly, what matters is the definition of a Duo deck.
"A deck that contains cards of two elements" would make this a duo deck.
"A deck that needs two different elements to play cards" would make it a mono.
I think the second definition is better, but that's personal preference.