What you're saving isn't a WebM. It's an MP4 with h.264 compression. The
browser knows this, and that's why it's choosing the appropriate extension
for you. All changing the extension to ".webm" does is makes it more
difficult for humans to tell what kind of file it is, and potentially make
some badly-designed software (like Windows) incorrectly identify what kind of
file it is. It's still h.264 regardless of what file extension it has.
Just save it with the proper extension, and if it bothers you so much to have
a file with a ".mp4" extension, transcode it as Magic Banana suggested.
YouTube does offer WebM for most videos (transcoded on Google's servers), as
well. They're lower-quality, though, so downloaders don't tend to choose them
by default unless you configure them to, and players don't tend to use them
unless your browser doesn't support h.264.
