(Your text, as presented in the mod, is in italics. The suggested sentence rewrite will be in quotes. Just general commentary will be in normal text.)
Enjoy the MOD while you can!
Consider simply "Enjoy the demo!" or "I hope you enjoy the mod in its current state!", as "while you can" comes off as being a bit...threatening? hehehe
Near their dwelling place, under the surface, lies another one of Jenka's buildings.
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This underground building is known as the "Temple of Unusuals," a horrible, torturous place.
"Temple of Unusuals" encompasses the entire name of the building, thus any punctuation should be placed outside the quotations - ie. "Temple of Unusuals", a horrible, torturous place.
Personally I would replace the comma between "horrible" and "torturous" with "and", but it does give it a bit more of a legend-y feel I guess.
This underground building is known as the "Temple of Unusuals", a horrible, torturous place.
The entrance emits a strange suctioning wind straight up from the center,
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allowing to seemingly catch anyone who happen to fly across it, pulling them right into it.
It was a trap devised by Jenka to catch an individual and pit them in a field of unusual things.
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As Balrog, having no clue on what has happening when they had felt turbulence while flying...
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The suctioning wind began to become fierce as if it were really trying to pull him in. Now...
In the first above section, consider changing "pit" to "put" - "pit" in its verb form means "oppose" or "fight". When swapping out "pit" with "fight", the sentence no longer makes sense - is Jenka going to fight the individual?
As for the second portion - from what I gather, you're trying to say that Balrog doesn't know that Curly has fallen, yet he is able to feel the force of the wind? "Suctioning" isn't a word, and not one I've typically seen people use to describe wind. We already get the sense that Balrog is being drawn in by the wind, but I think that being able to state what is actually happening rather than what
seems like is happening will make the statement more effective. It's okay to make a general statement in the introduction (imo); if there's more to what actually happens, then that will (or should be) explained to the player as they continue along in the mod.
The verb tense suddenly changes in the third section - it's quite easy to slip up, so be wary. Since the majority of your narrative is in present tense, we could make these two sections separate sentences, so something like
Balrog, unaware of (Quote and) Curly's current situation, begins to feel the wind's force as though it is trying to pull him in.
- or "draw him close" maybe. :/ I put (Quote and) because I'm not sure if Quote was also part of the falling scene. Also, consider putting "Now..." as the start of the next dialogue box sequence.
Quote and Curly Brace who were riding him encouraged him to flap his wings rapidly, but to no avail.
Wait, what? Quote was also with Curly? Oops, I almost missed that detail. The opening sequence, while very pretty to look at, also happens quite quickly. Additionally, with only Curly falling down the chasm, I assumed it was just Curly on Balrog. My bad.
I'm not certain on why this sentence makes sense at this point, but I can suggest making the verbs present tense (and place it in the order of when the events actually occur).
Quote and Curly Brace, riding on Balrog, encourage him to flap his wings rapidly, but to no avail.
The wind had surrounded everyone, and they were still trying to break free from the grip.
The wind surrounds everyone, still trying to break free from the wind's grip.
They both held on tight, but unfortunately the wind was too powerful for them to escape. Then...
Both, as in Quote and Curly? I thought Balrog was also part of the wind storm. "Both" implies there are only two individuals involved.
Consider:
They hold on tight, but, unfortunately, the wind is too powerful for them to escape.
They hold on tight, but the wind is unfortunately too powerful for them to escape.
or specifying "Quote and Curly" in the place of "They" if you are simply referring to the two of them and not Balrog (who are holding on tight).
Curly lost the will to hang on, and had fallen inside the Temple, which apparently closed off itself!
For better flow, try rearranging around the order of the clauses, like
Losing the will to hang on, Curly has fallen into the temple, which apparently closes off itself!
Now, at the very bottom of this dark place, she tries to find answers and her way out of here.
I feel like this would be more "punchline" worthy if it was just kept to "finding answers" or "finding her way out of here. And perhaps something more descriptive than "tries", like "seeks" or "struggles".
I think, overall, the whole awkwardness of the introduction mostly comes from the order of the sentences and how they don't really seem to flow. Try listing out the main points of sequence of events and maybe devising the introduction like that? Right now it seems to talk about the temple, then jump back to what happened with Curly falling, and it came across as being way too abrupt.