Unicode has emojis[0] which are freely usable for nearly every device as far as I understand.
What is the purpose here? How much overlap?
Aren't those all copyrighted? E.g. for the column "Appl" (sic) they're all copyrighted by Apple. You don't have rights to use them on your website or your Android app, for example.
Just because they're on the Unicode website doesn't mean Unicode owns them. It's just a resource to be aware of how emoji can appear differently in different sets.
Unless you can point out a column that is specifically open source.
The "Twtr" (Twitter) column, I believe, is Twitter's "twemoji"[1], which is CC-BY.
But your general point about the link being for comparison purposes and not implying any particular license is also correct, too.