Like i said, by these measurements, base64 would also be a cipher.

And people are telling you yes, they (rot13 and base64) are indeed ciphers. What's the confusion?

What people in this thread call a "key" is, not like a key, auxiliary input data, but hard-coded into the program. We are looking at encodings.

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.

Key can mean different things in different contexts. In a substitution cipher, the key is the mapping. In modern ciphers, the key would be some set of secret bytes. Everyone agrees that this cipher would be a bad way to encrypt/encode something. But using the word cipher like this has real historical meaning, and that is the meaning that is being used in the project.