Why does ozone disproportionate on reaction with potassium iodide?
The reaction equation does not really give information about the full mechanism, but one possibility is that the ozone is first reduced to ozonide ion, which is known in compounds with heavier alkali metals like potassium,; then the ozonide ion disprportionates to give diatomic oxygen:

$\ce{O3}+\ce{e-}\rightarrow \ce{O3-}$

$\ce{O3-}+\ce{e-}+\ce{H2O}\rightarrow 2 \ce{OH-}+\ce{O2}$

Note that the reducing agent is not specified as iodide ion.  Any mild reducing agent can act similarly.