Technically these are WEBP format. Are you using Eternity like the other commenter below? Checking from Eternity right now, it seems it does support animated GIF, just not the more modern/efficient WEBP format.
I have been creating them from scratch using the video editor Kdenlive.
The bouncy text is unfortunately a very manual process. Instead of simply creating a keyframe at the endpoint, where I want the word to end up, I create a couple additional keyframes several frames before the final endpoint keyframe. The first keyframe moves the text about 100px past the endpoint, then the next keyframe about 50px before the endpoint, then the final keyframe at the endpoint itself. This makes the text sort of "overshoot" and "overcorrect" as it approaches the endpoint, giving the bouncy illusion.
That is a bit of a high-level oversimplification, but I plan on eventually writing up a more in-depth tutorial on my technique.