yes, it's a shell..and no there's not even any semblance of correct anatomy here, but we think there's atleast the use of posture to emulate one.
There's no "ribs" per se, but in this skeleton version there's gaps between each of the rows in Bowser's shell unlike in his normal 3D model, therefore since this is supposed to be emulating a skeleton, we asume the intention is to signify ribs instead of a shell.