Do you combine your inputs with those of others when using XMR? You do. So it's a mixer. We can refer to the other users as "mixers" instead of attributing it solely to the network, if you're concerned about the semantics.
No it's not a mixer, and there is no anything centralized that could control transactions.
Even if you combine inputs of Bitcoin with other people it's not a mixer, joinmarket is not a mixer, mimblewimble is not a mixer, etc.
You invented your own definition of mixer that is not corresponding to reality.