... in the same sense that ROT13 or base64 would be a cipher.
Base64 is an encoding. It's an algorithm, no attempt at secrecy, thus not a cipher.
You'd do better debating this with a real life friend over a pint, rather than wasting your time trying to argue with multiple people here.
A bad substitution cipher is still a cipher. Just one you shouldn't use for anything important.
> with the help of a key
So, where is the key?
Maybe this differentiation is not popular or well accepted, but it was surely part of my cryptography curriculum and the following exam. I'd rather believe my prof than strangers on the internet.