The Help for key M-x key says
M-x runs the command execute-extended-command (found in global-map),
which is an interactive compiled Lisp function.
It is bound to <execute>, <menu>, M-x.
But in the global-map there is no entry for M-x, there are only entries for execute and menu. Where is the M-x binding present ?
You say: "But in the global-map there is no entry for M-x, there are only entries for execute and menu."
That's not true. If you are just using C-h v global-map then it's difficult to tell, unless you're good at reading the Lisp representation of a keymap.
Instead, load library help-fns+.el (Help+) and use C-h M-k global-map, to see a human-readable key listing for that keymap. There you'll see this entry, for M-x:
M-x execute-extended-command
C-h M-k is bound to command describe-keymap.
[Emacs 27 will also have such a command, based on the one in help-fns+.el, but the one in help-fns+.el is still a bit better, IMO. Some of the features of the help-fns+.el definition weren't adopted for vanilla Emacs.]
There is, however, another keymap variable that contains the execute-extended-command binding for M-x: variable esc-map.
Meta keys are in fact on that keymap. ESC followed by a key sequence is essentially the same as META followed by that same key sequence. So M-x is equivalent to ESC x. ESC is not a modifier key here; it's a prefix key.
When you see keys listed in *Help* you'll often notice ESC listed as a prefix key, and you'll see ESC followed by some key sequence listed as a binding.
And you'll see in the value shown for C-h v global-map an entry for ESC-prefix, which means that ESC is a prefix key globally.
