First, the fact that they're non-voting shares is because he wants to make a gift without altering the company. If they were voting shares, MIT might vote (in their interest) at some point to sell the company to another audio company or close the company and distribute the money it has to its investors so that they could invest in activities they saw as doing better for their endowment and long-term interests.
Second, by making the shares non-transferable, it means that MIT will be receiving income from Bose for as long as the company exists. While it's true that one can't deduct partial interests, I think there's a bit of leeway there. For example, Harvard's Weidner Library was gifted to the university with the restriction that if they ever knocked so much as a wall down, the library's ownership would transfer to the Commonwealth of Massachusetts. This was done in response to Harvard removing an earlier building that the family had donated. Now, I don't know if they deducted the library donation from their taxes and, frankly, the tax code is probably vastly different today. However, gifts are often made with conditions. If I donated a building to a university on the condition that they name the building after me, is that only a partial transfer since they can't dispose of the building however they like?
There's a good reason the law is in place. It prevents someone from donating the rent of a building they are unable to rent at market rates or sell as a scheme to make themselves money rather than being a true donation. However, Dr Bose's donation does seem like a true donation. He could keep the shares and not sell or donate them and then they'd be unrealized gains and untaxed. He's losing the dividend interest on those shares and so he is giving that up and MIT is benefiting from it.
I think this is more about legacy. It ensures that the majority of Bose shares will be held by MIT for all time. As such, the company can never face a hostile takeover. Likewise, it helps MIT which is an institution that he seems to care a good deal about - he received three degrees there and taught there for decades even as his business was successful. I'm not a lawyer and so it might run afoul of the letter of the law, but it doesn't look like a scheme in the way that many other non-full donations do look like schemes. This looks like a professor and founder trying to ensure the future of two institutions he loves.