Thanks for the patch.
The rename check seems to be to add an extension when we didn't know what extension to put in the tempname, not so much dealing with % or $.
But I'm not familiar with this code so I'm willing to merge as is :-)

Youtube-dl always creates a second partial file with the extension appended when ext is set. This change had to be accounted for when the escaped outtmpl was not the same as tempname, and the file was renamed. But renaming is no longer required because the actual flow would look something like the following, which does nothing.

outtmpl = tempname.replace('%', '%%')  # escape
...download...
outtmpl = outtmpl.replace('%%', '%')  # unescape
if outtmpl != tempname:
    ...rename...

The removed renaming code was merely to fix outtmpl escaping, and the real renaming (due to ext appending) is handled further down in that function. So this patch should be good, unlike the original fix in #838.

All clear, thanks!