Not being a gitlab user I'm surprised its notification are worse than github's, because it's not like github's notifications are any good. Between the comment notifications which don't link you anywhere half the time (possibly on inline comments? I never remember) and the update notifications which give you a completely empty diff on a push force, it only serves to signal that something happened on this thing you don't even care about.
All GitLab notifications are via email unless someone explicitly @s you. Furthermore, there is no api to notification. Basically, unless you monitor email, you don’t get notifications. It’s horrible.