GIF has the advantage of (usually) being lossless though, your WebM example has a lot of colour bleeding and noise going on and not much of a filesize advantage to make up for it.
To me it doesn't seem that bad in this particular use case. Text is still perfectly readable and acceptable to me for its purpose in this context. Heck, you enlarged that image just to emphasize the visual artifacts around the characters. And at that, compression settings more tailored to this purpose could improve upon that. GyfCat uses "well-rounded" settings for their more general use case of converting any/all GIFs to video. Since this is for a very specific use case -- terminal screencasts -- you could probably improve on visual quality while maintaining improved (smaller) file size by tweaking the compression settings.
Yeah there's certainly cases where video could be better, I was just being pedantic since you didn't mention you were comparing lossless and lossy methods.
I thought your example looked very blurry at first glance but maybe it's just because I'm used to ClearType-style font rendering.
https://i.imgur.com/O7E2WDq.png
Red text in particular will suffer a lot from compression algorithms designed for video.