Thank you for your messages. If you look here (definition 24 in the Random House Unabridged entry): high - WordReference.com Dictionary of English you will see that this meaning of high does exist in US English (Random House is an AE dictionary).
I doubt dry-aged is the same thing, Kelly. It's specifically about game. You are supposed to hang it until it's on the point of starting to rot and it's then (supposedly) ready to cook. It might not be that well known in the US, but to be honest, I imagine a lot of BE speakers wouldn't know it either. I suppose it's a lot to do with environment and what you do and don't eat!