If you notice here and there the site you are mentioning needs to be updated and fresh content added. It's a little an old website with information displayed not really updated
Not really. Actually, the last commit to the website was made 5 hours ago. You can see it here[1].
The thing is that someone needs to make a Pull request with Exodus added, so they can review the wallet and maybe consider adding it.
Btw, I don't think Exodus is open source. Which IMO makes it even harder to the them getting on that list.
[1]
https://github.com/bitcoin-dot-org/bitcoin.org/commits/master