There is an argument for brains working deterministically as well. We don't know for sure if they don't. A brain merely has hell of a lot more processes and variables to create differing outcomes for the same tasks compared to a calculator. So, no. A brain is not more like a glass falling. No matter how you try to make the falling glass analogy one with merit it just comes across as quite the stretch. With the falling glass analogy we don't have any artificial feature. The mechanism of it falling is part of the nature while the mechanism of a calculator is man made, hence artificial.
The two examples you give with water usage and dominos can be indeed described as AIs. Just in the very crude form. You seem to be thinking that just because something looks very basic it doesn't mean that it has no intelligence. It's not a threshold measurement. Its a spectrum. I understand that you needed to ignore what I said about abacuses completely to keep arguing against me but it's not exactly an effective way to argue. At least, Sir Adrian tried to address what I said. I would recommend you to follow his example in that specific regard.
How does a mechanism with an I/O system differ from a tool that has no mechanism? The answer is in the question itself.
The definitions I use are the ones existing in the dictionaries. I have been asking yours to see how it differs from those.