see now you're just splitting hairs and getting into philosophy. if your website will be stale tomorrow because you can't update it today, then that is a runtime dependency imo.
Yeah, I should have clarified I was talking with my operations hat on. From a development perspective, you might call it a "deploy-time" or "scale up" dependency.
If Github being down means you're not fixing your site today, I'd call it a runtime dependency.