Others have commented on built-in vim functionality for counting words, but assuming the author copy-pasted a similar looking command, they may have intended something like:
:%s/\w\+//gn
Knowing that you can execute a vimscript expression on each search match using \= is also cool and I was unaware of such functionality. https://vimhelp.org/change.txt.html#sub-replace-expression
Did you try it? Because that's not what it does. submatch(0) expands to the first submatch, which is the entire thing that's matched, and +1 adds 1 to this, which will a;ways result in "1" here since any string that doesn't start with a digit will be type-coerced to 0.
Anyway, /n being intended sounds likely; I forgot that would report the number of matches. Still very odd how that got morphed to what's in the article.
You can add it to your statusline (or tabline, ruler) with the wordcount() function:
---Aside: that "one-liner" doesn't "count the words in the file" at all? It just replaces all words with "1" and echos the last line number. I'm confused because this seems so wrong that I may be missing something? Unless the "67 substitutions on 5 lines" message is intended as the "word count", in which case I submit that 1) this is the ugliest thing I've ever seen, and 2) the author of this article doesn't know Vim all that well (there are so many better/easier ways to do this).