The apparent lack of a Christ figure is one notable difference from any form of Christianity. Another one is the apparent lack of sacraments - specifically the Eucharist. Also there are several notable things in the timeline. First, the Amarr are not the Unified Catholic Church (which in itself might be a New Age offshoot of Christianity - or an offshoot of the Church of the SubGenius, for all we know). They belong to a group called Conformists, which is a part of the Church. They settled on a planet, amongst others, and even then showed ambition for power by taking over the place, to lose power (and be kicked out, so possibly lose power violently) two hundred years later. Their exodus lasts for 1100 years - when they possibly splinter up. One of their leaders - but not their only leader - is Dano Gheinok, or Gheinok the First for "modern" Amarr. Eleven years after they have landed on Amarr, Gheinok has apparently gained control of the group and proclaims himself Prophet. For 61 more years the Conformists flock to Gheinok, before the EVE Gate collapses.
Now, this is possibly a big claim, but:
"And they stood before Him,
bathed in His light.
Yet their eyes were blind,
Their hearts rebellious,
And their minds refused the Lord.
Darkness descended upon them,
Spreading inside their minds,
And the flames of the Lord died within them.
Yet one flame remained,
And within this flame, the Lord found faith renewed.
Casting the others into obscurity,
The Lord turned to the one"
- The Scriptures, Gheinok the First 1:3
"And the Lord spoke to him from the heavens,
Described to him his holy purpose,
Bestowed upon him the wisdom,
Of Gods holy embrace."
- The Scriptures, Gheinok the First 2:8
"And so it was,
That Gheinok led his people on the great exodus,
To the land of our Salvation,
To the land of God,
To the land of his Chosen,
To Athra."
- The Scriptures, Gheinok the First 1:32
"By His light, and His will"
- The Scriptures, Gheinok the First, 12:32
Dano Gheinok is the Messiah. The Amarr aren't waiting for the Christ to come back, because he has already came back and led them to the Holy Land. It is AD 8000. The Communion isn't needed to get in touch with the Christ, because Dano Gheinok is out there, you can just travel to Dam-Torsad, or Aerui, or where ever he's staying and talk with him face to face. That is, if the growing theocracy lets you.
Now, that was then. There is some problems with meeting the Messiah in person, including the fact that Gheinok died. He might have lived hundreds of years, basically until his implants and/or the medical tech broke down. Those times are lost in the darkness of the history, but lots of people still stayed faithful through the Dark Age. The legends and the stories mutated over the ages. Until finally, the Amarr started to rise to new dawn, and Amash-Akura became Emperor. (I'd bet this happened roughly 8000 years after Gheinok died, just for symbolism.) Of course, not everyone accepted the new Emperor, but he fought. His political opponents were named heretics and followers of the Deceiver, and then the Empire was born. Not the modern Empire, though. More akin to old Judaism - they had endured the exile from the Paradise of Soekheviti, but finally they were led to the Promised Land of Amarr. They had endured the Dark Age, but finally defeated the heathens and heretics and claimed the land for their own. However, now everything was again well. It is around AD17000.
Three thousand years after the "Mayan Empire" was founded, technologically advanced people arrive from the Sea and make demands to the Emperor. The Amarr aren't overcame, though, and it might be that at first, there's no war, either - but it is clear that the Promised Land isn't the Paradise the people have believed. There's people elsewhere, and they're better off than the God's Chosen! This is the starting point for the modern Amarr Empire. They aren't having a hurry - they probably start to explore the planet, acquire advanced technology which they reverse engineer and possibly even improve, until finally - possibly with the help of the Khanid - they start the Reclaiming. That is why the Khanid wouldn't be enslaved. They weren't first encountered by an Empire looking to conquer anything it met. They were encountered by an Empire looking for allies to take down the Top Dog in the planet. It is now around AD 20000.
The next five hundred years, the Amarr conquer the entire planet. Udorian states first, then other nations - unknown nations, those Khanid nations who were not willing to join them, and possibly attempts to brake away from the Empire. (It is noteworthy that the Minmatar reach a global culture before the Amarr.) Their technology has likely reached the current real-world level or surpassed it. Within the next seven hundred years they explore the nearby starsystems, culminating in the building of the Amarr-Hedion stargate in 21290. At this point, they likely start to receive radio transmissions from other nascent civilizations, ultimately leading into conquering the Ealurians less than 150 years laters. The connection to the Holy Land, however, is starting to crack. The old dogma doesn't fit.
The Empire at this point is rather damn big. Likely there were many civilizations to the galactic east - Takhmal, Ealur and others, since the Empire seemed to have first stretched there. The City of God is built around the same time as the conquest - Reclaiming - of the first non-Athran civilization. Elevated by recent conquests, the Emperor (Zaragram II Ardishapur) proclaims himself God, and we know how well that ends. Apostles come to power once again. Possibly even try to return to the Holy Land type of think, but four hundred years later the Apostles lose power again - only a few generation changes in power for long-lived Holders (even if there must be several generations of noble sons between generations who are actually in power unless the Amarr have very good doctors to keep the old Holder's pecker going).
With the nobles - the military and industrial elite - back in charge again, the Amarr continue to expand their Empire. It is noteworthy that before Amarr-Minmatar first contact, the Minmatar have been in space for almost a thousand years according the current timeline. The Amarr must've been able to record the gravimetric activity caused by their gates. Perhaps they've been careful for this reason, since Pator isn't that far from the City of God, the old center of their Empire. However, they go to the entirely different direction and take Aridia (and likely, Kor-Azor). Ni-Kunni are Reclaimed around the same time as the Amarr start to raid the Minmatar. In the next 125 years, the Minmatar are weakened enough - and the Amarr are sure enough that they know exactly what the Minmatar have - that Amarr take over the superiority in the three systems. And here comes an important retcon I just noticed: In the new timeline, Amarr don't conquer all of Minmatar, as previous timelines suggested. They conquer only Matar in 22480.
Since then, it is likely that the Minmatar rebels nick all kinds of stuff from their Amarr masters and expand before the Amarr catch up with them and conquer their worlds one after one. The timeline has lots of errors, of course - for example, the Amarr apparently invent jump drives after Khanid secedes (so apparently early Amarr titans could use jumpgates, or then Khanid warped his titan between systems). The Amarr likely meet the Gallente first - possibly because the Minmatar are just trying to hide from Amarr, but Amarr might be still looking for more civilizations to take over. The Gallente eventually learn of the Minmatar and start to help them to cover their flank. Minmatar have, at this point, spread over their current-day territory, though Amarr control the most of it. The Minmatar have a huge covert buildup of military strength - the Elders and Shakor would be very, very jealous (and that time, they didn't need to keep it secret from the Gallente, either) - culminating into the open rebellion, where the Amarr - used to attack not defend, and bombard planets not fight for space superiority - lose.
I got a bit rambly, but the main point is that even if the Amarr faith had at one point have been Christianity, it has had several important changes over the years - Soekheviti as the Promised Land, exodus, diaspora, Athra as the promised land, Messiah Dano Gheinok, the Dark Age, Amarr (continent) as a Promised Land, Udorian contact and rapid adaptation to new technology, and finally the Age of Reclaiming. And then, finally, stepping into the stars. Until the new Reclaiming, the Mad Emperor, brief period of Apostle rule, and then the modern Amarr Empire. That's at least ten events that must have brought at least Reformation-level changes to the faith.