I completely agree with AvienMael. It is aesthetic. I believe I have enough whistles from the high end on down to safely say that I can find no relationship between the mouthpiece angle and the sound of the whistle. Although, in my humble opinion, the steeper the angle, the more difficult it is to play the instrument since, (again IMHO) it can be more challenging to control, unless one places the mouthpiece further back in the mouth which is never a good idea.
This is a feature of the Ormiston whistle - the windway entrance is cut at an angle. And it can be annoying at first, since your lower lip tends to close the entrance. But... it has an unexpected effect: playing the whistle angled very downwards gives a quieter (although much breathier) tone, which can be handy. You only get the full, quite pure tone by blowing the whistle at around 45° or higher. When I started out with this whistle, I was surprised by how variable the tone was, and it took a while to realise what was happening.
Phil Hardy gave the Ormiston quite a negative review on his website (one of the few whistles he hasn't been quite positive about), and the mouthpiece cut was his main gripe. He also said that there was "something missing" from the mid tones. I'd agree with him, but it's a whistle that takes a little getting used to. Angle is the key to a full tone.
This is only anecdotal, of course, and I don't know how far it applies to other whistles cut this way.