Robert Levin states that Mozart improvised and has devised his own form of Mozart-like improvisation. What is known of Mozart's improvisation technique?
By law of averages, it's very unlikely that Wolfgang Mozart was unique (this is quite a shocking statement, I realise). There were a lot more working composers of the age who's work hasn't survived, and a great many again who's work is known, but obscure, and not considered part of the classical music cannon.
Of these, most will have been following the prevailing rules of music theory and imitating the music they were hearing which was popular, and therefore made money. The idea of a composer being unique suggests their work doesn't overlap with any other, which is incredibly unlikely.
As for improvisation, there are some historical documents which suggest he was an improviser, which a lot of composers are. While it's possible to write a piece purely by the rules of composition (accepted harmonic progressions, structure, etc.) you're unlikely to settle on a result without actually hearing it, when you sit down at a piano and play some music, you modify it, improve, try playing on beyond what's written... In short, improvising.
But you're asking about an improviser from before the age of recorded music, we only know what was written down, not what was played before it was committed to paper. In truth, we have no idea how he went about improvising.