If Airplay Mirroring is the only feature you wanted on Mountain Lion, and you were expecting it, call AppleCare, ask to be transferred to Customer Service, explain your unhappiness and they will refund your money. You will then need to remove Mountain Lion and go back to Lion. Problem solved.
Your iMac is in no way obsolete. My MacPro that will not run Mountain Lion at all but it is doing everything it has done for me since I've had it. I plan on continuing to use it. Claiming that a computer is obsolete because it cannot run one new feature that was introduced through new hardware is just silly. That is like saying since my car can't do the automatic parallel parking it is obsolete.
Would you feel better if Apple, when the new Quicksync was made available to them, had said, "This won't be fair to all of our customers who purchased Macs before this was available so we just won't write the software to enable it and won't let anyone have Airplay Mirroring?"
There will ALWAYS be new technology, new CPUs, new chipsets, and they will do new things for people who buy them. People who have older cars, TVs, computers, smartphones, GPS units, etc. won't have those features until they upgrade. That is a fact of life in technology. And it has nothing to do, in this case, with how much you paid to buy yours. Intel had not yet released Quicksync when you bought yours.
You probably can find a 3rd party repair site in your area, or online, that will replace the motherboard in your iMac with a newer model (if it will fit) that will give you a new Intel chipset. The motherboard will probably cost you about $1100 and they you will have to pay for the labor and buy new RAM. If you have AppleCare that will be void.
Or you could sell your iMac and use the proceeds to buy a new one that has the Intel Quicksync chipset. Even if you have the slowest of the iMacs from mid-2010 you can get $428 from here: http://store.apple.com/us/browse/reuse_and_recycle and selling it outright you would proabably get twice their estimate.
This issue, as has been explained to your repeatedly, cannot be "addressed", so you might as well pack up now. But don't go to Dell, HP, Toshiba, or any of the other big computer companies. They also use custom parts and cases and their machines also can't be updated (they all have computers out now that can OTA mirror but they don't call it Airplay but their older models cannot be updated to do so). Your best bet if you want to be able to update without buying a new machine is to custom build your own computer or go to a shop that does custom builds. Specify a standard case and you should be able to update the motherboard as new chipsets emerge.