"continue_outer" is not valid code. I assume you mean "goto continue_outer".
is equivalent to
only because the label is at the end of the loop. That mightn't apply if you changed the code after the label, but then it would be a different example. As implied by the comment, the continue_outer label should point at the end of the block.
does nothing other than provide a target for the label in older versions of AutoHotkey_L. Would it help to remove this long-obsolete line and add a comment clarifying that the continue_outer label should point at the end of the block?
As my example shows,
The original example shows exactly the same thing, but additionally shows how it would be done with goto.
not similar to break, as the doc example seems to imply.
I don't know where you got that implication.
skips to the end of the current iteration, and execution then flows into the next iteration (if there is one), like continue.