No it's not a mixer, and there is no anything centralized that could control transactions.
According to theymos' definition, that may be the case. But, in my understanding, if a tool is utilized for coin mixing, it qualifies as a mixer. And if it lacks a central point of failure, it can be considered a decentralized mixer.
You invented your own definition of mixer that is not corresponding to reality.
Really? Then what term would you use for a protocol that mixes your inputs? A "joiner"?
If mixing is the activity, then the mixer is the entity performing it.