> In the Emacs manual, page "Major Modes" appears the following:
>
>     all programming language modes run `prog-mode-hook', prior to
>     running their own mode hooks.
>
> I suggest amending this sentence to something like:
>
>     many programming language modes (including all these distributed
>     with Emacs) run `prog-mode-hook', prior to runnuing their own
>     mode hooks.

+1.

But: these -> those,
     runnuing -> running,
     and we can drop the comma before "prior".

And I'm not sure why we need to or should say "(including...)".  Why?

I'd suggest just this:

  many programming language modes run `prog-mode-hook' before
  running their own mode hooks

Or even "some" instead of "many".  What does it matter how
many do this?