It just doesn't add up. They are not explicitly saying that the Mini 2 is also an iPad Air, but the specs suggest that it is. They could have changed the messaging entirely, saying there are now two iPad Airs - a 7.9" and a 9.7". But they didn't. What are they not telling us?
You have some good points, but in my opinion you are overthinking things. Apple are in my opinion trying to
simplify things, not complicate. They use the same processor, the same exact resolution and same graphics chip in both their premium iPads. This also holds true for the cheaper variants (iPad 2 and mini 1) This means that they can mass produce the hardware more effectively, software developers can develop for two ipad resolutions instead of three (ipad 2/mini 1 use one resolution and iPad 3,4, Air and mini 2 use another) and there is less fragmentation overall when it comes to hardware .
More importantly it simplifies things for the customer. The only thing they really need to consider now is
price vs size. Pay more to get a physically larger screen.
In the lower end you have the ipad 2 and mini 1 with about a 70 dollar difference in price and 2 inches in size, and on the higher end you have the iPad air and ipad mini 2 with a 70 dollar difference and 2 inches in size. Do you see?
EDIT: The price differences might be off here, I'm from Norway and I don't have full understanding of the US prices. But hopefully my point still stands.
I actually think this is a really smart move from Apple's part.