Man I'm sorry this crit slipped my mind.
The sun beat down on the gathered crowd, warm, gentle rays becoming blistering heat.
Now this never specifies when the warm gentle rays become blistering heat. I see some thematic motive to this sentence, so don't mess with it too much. Just specify. Something like: "the warm, gentle rays present just hours ago becoming" etc etc.
Sweat trickled down people's faces, but they didn't care.
Why didn't they care? This sentence seems a bit jarring. We've already established that it was hot.
One, was their king.
And the other was..? I'd advise adding something like "The other was his executioner."
For a shadow was over him, a man stood before him, holding a metal sword over his head.
So this is redundant in many ways. Something simpler, like: "For a shadow was over him, holding a sword"
And dead.
Most headless people are. If this is shooting for levity, a bit of gallows comedy, i'd say you're good. Otherwise, it's unnecessary.
They were excited, staring at the center, waiting for the single strike that would bring this mighty man down.
I'd specify something like "once-mighty"
The peasant- Their peasant- Would now become king.
Are these supposed to be capital? when you use em beforehand they're lowercase.
His headless corpse sank to the ground-
Now, he was no longer a king, not even a peasant-
I'm not too sure what you're doing with those dashes at the end… You end a lot of sentences in them and I really don't think that's correct in any way. (side note if you do -- it'll come out at —, which is a proper em dash)
But it mattered not, for now, he was nothing.
I would italicize 'now'
It really was a hot day.
Ehh. This doesn't really stick the landing. It hurts the flow. Speaking of…
— — — —
Are you familiar with musical notation? Writing a piece of literature is much like composing a musical work. Different styles, expressions, louds and softs, etc. etc.
In musical notation there is a device called an accent. It makes the note loud, sudden, and abrupt, and can add great contrast to a piece. This piece, however, feels like it's all accents. It comes off as rather dramatic
stanza after stanza. All intensity all the time. There's never a place for the reader to catch their breath.
Flow and voice are the hardest things to nail down in a work. I personally believe in this case your line-by-line formatting is overburdening you here. To add more flow, more legato to this work, I'd maybe do some larger stanzas.
And to answer a question: No. Works on WL don't need to be supernatural at all. One of my favorite authors on the site, 
lzhoudidion solely writes what I might call historical fiction. Anything fits here, as long as it inspires a sense of wonder (though even that is a rather flimsy rule).
Otherwise, your themes are on point. Word choice could use some polish but I feel there's some motif-ing going on there so I won't be too scrutinizing, and it's otherwise pretty solid.
