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What are the products of the reaction: $$\ce{K + SO2->}$$ Here, $\ce{S}$ is in $+4$ oxidation state. Hence, $\ce{SO2}$ has both oxidizing and reducing character. $\ce{K}$ is a stronger reducing agent and hence, it will reduce $\ce{SO2}$.
So, $$\ce{K + SO2->KO2 + S}$$ is a possibility.
But the answer given is $$\ce{K + SO2->K2SO3 + K2S2O3}$$
$\ce{KO2}$ is definitely out of question. True, it does form when $\ce{K}$ reacts with $\ce{O2}$, but that's another story. It is a peroxide (in a broader sense), so it contains oxygen in oxidation states other than -2. $\ce{SO2}$ contains oxygen in -2. Who is going to oxidize oxygen?
Turning down peroxides, we resort to the more realistic option of $\ce{K2O}$. Now, that's a basic oxide, and $\ce{SO2}$ is an acidic oxide. Surely some chemistry is going to happen between them.
As to where the reduced sulfur would go, it is not quite clear and depends on many things. With excess of potassium one might expect ending up with $\ce{K2O}$ and $\ce{K2S}$. Obviously that's not our case. Then we must consider a reaction between $\ce S$ and $\ce{K2SO3}$. Such reaction is known (though probably under different conditions than we have here) and indeed produces thiosulfate.
That being said, partially reduced compounds of sulfur are numerous and I see no reason to favor one above the other without some deep investigation. Have you heard about dithionites, for example? They are known to appear when reducing $\ce{SO2}$ with certain metals; why not here?
