The processors they're using appear to be well in excess of $10,000 each. To get 224 physical cores, you'd need to run them in a 8-CPU configuration, so you've got ~$100,000 invested just in the processors alone.

Memory is absurdly expensive right now, and I'd be shocked if 12TB of it cost any less than another $100,000.

You have to sign a multi-year reservation, and with a cost of $267,512.88 per year (as calculated from another comment in the thread), I assume their profit margins for the first year are nearly non-existent. However, over the course of the remaining two years of your reservation, they're making a great deal of money on each reservation.

So yea, I imagine someone could build something like this, but such an individual would need to have very deep pockets.