Classification of a stream cipher
Logically I think that should also be a synchronous stream cipher. The word refers to the fact that the keystreams must be synchronized between the encrypter and the decrypter to allow decoding. With anything other than a self-synchronizing cipher that is the case.

However, that does not mesh with existing usage. You will find many texts (example) saying that with synchronous stream ciphers the keystream is independent of the plaintext and ciphertext. So you should definitely not use that term.

Asynchronous is not very good either, for the reason you mention, but you will find it used to describe such ciphers (e.g. Helix here, pdf). So that is probably more understandable than calling them synchronous, even if it too can be confusing. 

If you need to write about it, I would avoid the issue and just call it a stream cipher with a plaintext-dependent keystream. You can say that it is not self-synchronous if you need to make that distinction.