Why did the two characters get hanged?

We aren't told exactly why the two men were hung, but from the text, we can infer that they were responsible for lawlessness.

In point of fact, Poker Flat was “after somebody.” It had lately suffered the loss of several thousand dollars, two valuable horses, and a prominent citizen. It was experiencing a spasm of virtuous reaction, quite as lawless and ungovernable as any of the acts that had provoked it. A secret committee had determined to rid the town of all improper persons. This was done permanently in regard of two men who were then hanging from the boughs of a sycamore in the gulch, and temporarily in the banishment of certain other objectionable characters.