It's a great move by Twitter, but it's a pity they didn't make the images GPL compatible. According to the licensing section of the GitHub repository:

Code licensed under the MIT License: http://opensource.org/licenses/MIT
Graphics licensed under CC-BY 4.0: https://creativecommons.org/licenses/by/4.0/

As previously discussed on the tavern, the CC licence (apart from CC0) means the emoji images can't be included in a GPL plugin or theme.

Fortunately, it looks like the images are served via Twitter's servers, so from my reading of it, plugins and themes using Twemoji can remain 100% GPL. Still I wish they'd gone with a GPL compatible license for the images!