Try and re-install the manual page itself: see https://askubuntu.com/a/244810/15811

Because ... After I did this I got the normal manual page:

$ sudo wget https://yt-dl.org/downloads/latest/youtube-dl -O /usr/local/bin/youtube-dl

$ sudo chmod a+rx /usr/local/bin/youtube-dl

First page:

YOUTUBE-DL(1)                                                    YOUTUBE-DL(1)

NAME
       youtube-dl - download videos from youtube.com or other video platforms

SYNOPSIS
       youtube-dl [OPTIONS] URL [URL...]

DESCRIPTION
       youtube-dl   is   a   command-line  program  to  download  videos  from
       YouTube.com and a few more sites.  It requires the Python  interpreter,
       version  2.6, 2.7, or 3.2+, and it is not platform specific.  It should
       work on your Unix box, on Windows or on macOS.  It is released  to  the
       public domain, which means you can modify it, redistribute it or use it
       however you like.

OPTIONS
       -h, --help
              Print this help text and exit

       --version
              Print program version and exit

Though it does not matter much: you can get the same information you are asking for when doing:

youtube-dl --help

Since I knew that using apt-get install youtube-dl installed a working manual, I re-installed using apt-get, copied the manual /usr/share/man/man1/youtube-dl.1.gz and put it into /usr/local/share/man/man1/. Then I did apt-get remove youtube-dl. Now, the newer youtube-dl program that I installed using wget is referring to the old manual page that I took from the apt-get version (which is now removed). Formatting is all correct too.

Probably not the best way to do it and the documentation is probably outdated. But for the basic options, it will do for now.