The instructions at the top of the page encourage you to hot-link directly to the images they host. It would be hard to say sending them a ton of traffic is "abuse" when they literally suggest you do that.
In general though hot-linking across domains like that is bad practice because the content on the other domain might change in a way you don't like. This was a pretty common practice for a while: https://tvtropes.org/pmwiki/pmwiki.php/Main/HotlinkedImageSw...
If those images turn out to be important to your project such that http.cats going down would be an issue, absolutely you should serve a copy of that content from your servers (assuming all the copyright licenses are in order).
I’ve been a big fan of this site since it was introduced to me when I first learned to code. But to your point, I can’t really imagine a scenario where it would become an ‘integral’ part of an project.
For use in development & testing, sure. Or just as a goof to one of your coworkers. Honestly, I’ll admit I’ve used it countless times over the years to refresh my memory on a particular code, while knowing I’ll get a nice giggle of from it.
But in the scenario you are asking about, in an important production environment, you would be wise to cache the images and serve them in your method of choice yourself. Or better yet, just clone the repo and add install it on your server. It’s MIT licensed, so no worries as far as getting in trouble. Problem solved! :)
In general though hot-linking across domains like that is bad practice because the content on the other domain might change in a way you don't like. This was a pretty common practice for a while: https://tvtropes.org/pmwiki/pmwiki.php/Main/HotlinkedImageSw...
If those images turn out to be important to your project such that http.cats going down would be an issue, absolutely you should serve a copy of that content from your servers (assuming all the copyright licenses are in order).