I'm primarily an Android user who just bought an Air 2 due to there not being many good options for large Android tablets right now. I've owned lots and lots of devices over the years...smartphones before they were even called smartphones, tablets, even a Cybiko (look it up). I'm also working on becoming an audio engineer in the music industry. Here's my perspective on this...
Firstly, these speakers are ridiculously powerful for their size. I've never owned any smartphone or tablet with a louder set of speakers (haven't owned any of the HTC Boomsound devices, so I couldn't say if they are any louder). Not only that, but they sound pretty good too. They seem to have a bit more oomph in the lower end than even my 15" 2012 MBP, which is saying a lot for a tablet.
So let's take that into consideration for the moment. Also realize that not only are they in a device that's a solid, thin sheet of aluminum and glass with no give anywhere, but these two fairly powerful mini-speakers only have 28 pinholes with which sound can escape into the air from. The rest of the tablet, if it were more hollow inside, would act as a chamber and dissipate the air vibrations (since sound is literally vibrating air).
All in all, this behavior is very normal. The speakers are not only powerful but are a bit more full-range than what is usually placed inside of a tablet or laptop. Since the Air 2 is built so rigidly with very little open or wasted space inside, and there isn't much room for the sound to escape outside, the tablet will vibrate accordingly.
Now, whether or not this is too annoying for you to deal with is a personal thing, and I do understand if some people would find it annoying. But it's not a defect, nor is it a design flaw. It's just how vibrating air works. Building a device, any device, is all about compromises. Apple wanted to make the Air 2 thinner, but not compromise on perceived sound quality. They could designed it with smaller, less powerful speakers, and made larger holes with old school mesh covers, and that would help things. But it would compromise their design choice.
The reason I mentioned that I was an Android user is because I see how many people are attacking others here for being "Apple shills" or "fanboys" for trying to explain this. I'm as far from an Apple fanboy as you can get it, and I still think iOS is terrible compared to Android. But this isn't an "issue". It's how it's supposed to work. And, if the tablet were not vibrating, the sound quality of the device would change as well. It would not sound like it does right now. My best guess is that the way it's set up now allows for a perceived increase in lower frequencies.
Honestly, if it's a deal breaker to you...return it. Because it's not something that needs to be "fixed". Only way Apple is going to "fix" it is by using smaller, less powerful speakers, or making the tablet thicker with more space inside, or creating larger holes for the air to escape directly out of the tablet. All of which I don't see them doing, since their design philosophy seems to be lighter, thinner, simple, and elegant.
*shrug* Just my two cents. The speakers sound great to me.