He killed Nicholas first as a rival, and second as an opponent (they were, you know, on opposite sides during the war, if you hadn't noticed).
Demonic principles and the tenets of Chaos.
The developers presented you with an exotic picture of a demon's inner world, his internal struggle, feelings, passions, life priorities, etc. Against this backdrop, he does something today, and tomorrow he won't be able to explain to you why he acted that way (because at this critical moment, his principles (Agra'il's) change almost every hour, and you ask - why did he do this first, and then that...
And don't we always know exactly what we want when we undertake something (intuitively)?
Agra'il/Rai'lag's story is beautiful and realistic, and you (probably based on some templates in terms of game storylines) are criticizing it.
Nothing personal.

Allow me to disagree with your concept of Agra'il. Although he is a demon, he is somewhat not demonic. The fact that the Griffin Heart did not affect him, which should create a portal for demons to Shio, is already a sign. In my opinion, Agra'il was initially conceived by the scriptwriters not as a true demon, but rather as a demonic personality (unless we consider the possibility of his mission as an opportunity for the player to play on the side of Hell). That is, Agra'il is not a true follower of Chaos, but only pretends to be. Then we return to the question - who is he originally? And regarding the logic of the creations of Chaos, I think you are overthinking it. Kha-Belekh (seemingly the very embodiment of Chaos) acts strictly logically. And all the armies of Hell are subject to strict discipline and subordination; otherwise, they would attack the enemy wherever and whenever they could, and not in battle (although, of course, one must adhere to the framework of a turn-based strategy). And in general, it seems to me that Hell is not Chaos. So many writers have broken their pens writing about the struggle between Chaos and Order that it is wrong to equate Hell (Inferno) and Chaos.
But let's get back to Agra'il.
@The developers presented you with an exotic picture of a demon's inner world, his internal struggle, feelings, passions, life priorities, etc. Against this backdrop, he does something today, and tomorrow he won't be able to explain to you why he acted that way (because at this critical moment, his principles (Agra'il's) change almost every hour, and you ask - why did he do this first, and then that...
And don't we always know exactly what we want when we undertake something (intuitively)?@
After meeting with Tieru's illusion, Agra'il, despite all his spiritual quests, acts strictly logically. So, accusing him of a lack of logic, I think, is unfair to Agra'il. He is purposeful, persistent, and resourceful. This doesn't quite fit with your image of a demon who is confused and acts under the influence of momentary impulses.
P.S. And this is no longer about the game. Greetings to my neighbor. I only noticed the address today. I am also from Bishkek.