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Where is the point? How is this story at all new, moving, or interesting?
Let's start with the unnecessary part of the story, which is most of it. Four fifths of your story is wasted prose. You take three paragraphs and a header to say "As of 10/07/39, Arecibo 2 has received transmissions [from 16 Cygni] directly relating to the SETI broadcast 140 years ago." Everything else is either implied or irrelevant.
Moving on to internal consistency, this is not how a top-secret email reads. Neither Director [name redacted] or Director [name redacted] need to be shielded from knowledge of each others names. Nor, unless there are multiple directors of their respective organizations, is this redaction even meaningful. We also see that Director [name redacted] fails to include either a greeting or a signature when writing to his ultra-mega-superior. At least the aliens said [untranslatable hello].
As we move on to the transmission itself, we stumble over several more consistency issues. How does the government plan to keep a broadcast presumably powerful enough to reach Earth from being discovered by random private observatories along the way? What with the first contact with alien life and all, I'd think there would be amateurs pointing their receivers at 16 Cygni. For that matter, how is this the first transmission from the Transcygnists? Between the time the SETI signals reached 16 Cygni and the time the Transcygnists send their mega-transmission, there's bound to have been prayers, talk show debates with the Humatheists, references in their radio comedies, advice for chopping off unhuman appendages, etc. This had to be in the previous corpus, so how is the existence of the Transcygnists supposed to be a surprise?
[alien concepts/ideas/thought] inexpressible in [English/human speak] is [negative] a new [concept/thought]. [pronoun] is also [irritating/painful] to [read/understand]. It also [negative] [makes sense/fits] [here/current location], because how [did/activity] the [translators/scientists/linguists] [figure out/discover] [article] [meaning/shade/nuances]? For that [topic/mass-energy], why [did/activity] the [translators/scientists/linguists] have some parts in [English/human speak] and others in [alien concepts/ideas/thought]?
This is not how an alien message asking for aid from the Space Gods would read. Where is the praise? The asking of forgiveness for insufficient Transcygnist progress? Why are they complaining about the process of humanification, instead of boasting how far they've already come? Why are they talking about the position of the Humatheists instead of asking the Space Gods to smite the [heathen/unbelievers/unwilling]?
Let's stop and think about the theme, however. Suppose SETI today received a transmission from aliens, containing alien DNA. Which would Joe Q. Public think:
A) "OH MAN! SPACE ALIENS! WHAT A DISCOVERY!"
B) "OH MAN! SPACE ALIENS! TIME TO SOW A TRUNK ONTO MY FACE AND INJECT SPACE DNA INTO MY BLOODSTREAM!"
And how is Xlorbothek 9. Alien going to react any different?
We end with the destruction of the story's meaning with the aliens. If you stopped at the message, you would leave the reader with a moral question: what do to if aliens start worshiping your species? This is perfect for flash fiction. Instead, the question is rendered moot by the nonexistence of any aliens.
WARNING WARNING RANT LEVEL INCREASING WARNING WARNING
If you're trying to create something people enjoy, I'll be blunt: Drop the overused "Religion and its adherents are evil/stupid" cliche, lock it up, and never use it again. It doesn't even matter if you didn't intend to say anything of the sort. It gravely offends the majority of the world's population, preaches to the choir of those who don't like religion, and boring those in the middle to tears. There's at least one magazine and one anthology which will reject such stories out of hand, and neither is religious.
It's one thing to say "This thing is evil, and evil people worship it.", because both believers and unbelievers hold there to be evil things people falsely worship. It's another to say "Religion in general is evil, and people who worship are evil", because that's the overdone cliche. It is better to maintain balance, and have good people who are wrong and evil people who are right. Better still to have neither good or bad people, but people who have chosen their path, and may yet stray from it, for such is reality.