given some pure machine language commands, for example the following bytes:
1011100010011010000000100000000000000000
11000011
(taken from: How to write and execute PURE machine code manually without containers like EXE or ELF?)? I understand that in general there needs to be a .EXE, ELF, or .OUT wrapper, but as far as I know these formats are platform-specific just to be able to double-click and run them.
Does there exist a file format that can be double-clicked across windows, linux, and mac, and run the same machine code (assuming no external dependencies) ?
Does there exist a file format that can be double-clicked across windows, linux, and mac, and run the same machine code (assuming no external dependencies) ?
The short answer is no.
The longer answer is that you are mixing concepts and levels of abstractions: double-click is not an OS-level concept, and no OS runs a binary in response to double-click.
They all run a binary in response to execve or a CreateProcess system call, and there is no universal file format that will be acceptable to the OS on all of Linux, Mac OS and Windows.
how does unity's "windows, mac and linux standalone" game build work
In the same way a Python foo.py file works on all platforms: there is a native binary which interprets the code contained in the game. The native binary has different file format on each platform (ELF on Linux, Mach-O on Mac, PE on Windows).