

To me, it is not. If the internet or anything else goes down you lose all access. You are not hosting your services, so claiming to be SELF-hosting is not really accurate.
Furthermore, in the phylosophical aspect, you depend on a private company for all your infrastructure and are not doing anything against the centralization of the internet. To me, this is one of the core reasons I self-host. Maybe we need to make new terms for this, but allowing anything under the corporate cloud umbrella to be called SELF-hosting seems bad to me.
Conclussion first: In any case, I would agree with what some other used said: What we care about in here, for the most part, is the software element of it. Even if I personally don’t consider using Cl*udflare to be self-hosting, all of us have similar info sharing interests, so this is just a terminology argument that does not really impact us that much
I wrote this first: Actually, this is a pretty interesting thing to think about. To me, the key factor to distinguish what is hosting and what is not is the use of a server. I would say that internet connection is not a requirement for hosting, otherwise it seems absurd to deny that the servers of big LAN parties like the Euskal Encounter are not hosting anything, they clearly are. Down to the smaller scale, having a LAN only Minecraft server in your home server, I would say it still is hosting, even if only you and your family use it. Now, going to a non dedicated computer that is exposing it on LAN, is it self-hosting? I would say no, just because it also seems absurd that any single player world opening in LAN to enable admin suddenly is self-hosting, I say it is not.
But I guess this shows that there is a point where we need more specific definitions, there is some ambiguity.
A summary of my definition attempt: