I would argue ROT13 isn't encryption as there is no key (it is just defined within the algorithm). Simple XOR with a constant is (bad) encryption and the constant is the key..
The Caesar cipher is encryption because the shift is the key.
I think josephlord's point was that the name "ROT13" completely specifies the 'key': If you changed that, it would no longer be ROT13. So it arguably can't be considered a key if you define 'key' to mean 'a piece of information additional to knowing the algorithm used that is necessary to decrypt'. (If the 'algorithm used' was specified just as ROT (i.e. caesar cypher) then 13 would be a key). But this is basically semantics.
The Caesar cipher is encryption because the shift is the key.