Looks to me like you could get 50. (I think you can get 9 bottles, not 16, in one of the full diamonds.)
Edit: Now I am not so sure. Realizing that the carcass of the cabinet is 36" wide, and allowing for some wood thicknesses, and doing a little geometry, it would be very close to fitting 16 Bordeaux bottles in each full diamond. I estimate that the interior of the diamond is about 11.5" on the square part. Narrow Bordeaux bottles are almost exactly 3" (but "fatter" ones range up to 3.25").
But, with small diamonds, a miss is as good as a mile.