Any machine which is Turing complete is Tetris-complete and all the other -complete you list. At the end, all of it is just binary values somewhere and trapping instructions which you can perfectly run on anything Turing-complete.
Paradoxically computation is actually just small part of what computers do.
It only talks about binary choices, but keyboards are just methods for sending a few of those at once.
If you don’t abstract away that kind of stuff, it’s not obvious why you’re doing any generalisation at all.
Tetris.app on my phone cannot read from a game boy cartridge, or speak to a joystick or arcade cabinet CRT screen - is it Tetris complete?