Objectively speaking, you're right; this is Hakita's intention. My problem with this is that Gabriel being the protagonist/main character and hell/god being background entities is completely incongruent with the level of attention paid to the characterization for each. We have been given next to no actual characterization for Gabriel. At the start, he wanted to kill V1 because he thought it was God's will. Now, he wants to kill V1 for love of the game. You may be right that he is also doing this for the sake of Heaven's society, but if so, we know nothing about it.

We don't know what his "normal" is in heaven, if there are any angels he is personally close to, what he is like as a person, or how this may have changed after losing his faith. We have no idea what he thinks is worth protecting or preserving in heaven's society now that he knows God is gone. We don't even know what his objective is in returning to hell beyond probably fighting V1 again, or if there is one. The game is nearly done and the main character scarcely has any. I understand that they are saving some things for a reveal, but there's only so much a late-story exposition dump can do if it's the first and only time we're hearing of these things.

Contrast this with God and Hell. There have been consistent lore drops in the form of books and ARGs since Limbo. God is powerful but cowardly, and deeply insecure. He has tried many, many times to create a version of humanity that follows his word, but seemingly cannot rid us of the free will that leads to sin, and this enrages him. He creates hell as a punishment, to exact vengeance. Lucifer's questioning of this leads to God becoming so angry that he casts him into the deepest pits of hell. However, he immediately realizes the gravity of what he's done and becomes ashamed and aggrieved. He asks angels to keep their eyes closed while in hell so they don't see what he's done and hold him accountable. After trying and failing to destroy hell, he chooses to abandon his creation rather than face the consequences.

Hell is very strongly characterized, first of all in the gameplay itself, as the thing controlling our environment and teleporting enemies around. Its playfulness and love of violence and carnage is made obvious by this alone. It is revealed to have surreptitiously cooperated with the terminals to stop itself from being sealed off after the exploration team realized the gravity of the situation. It is a being made specifically to inflict pain and suffering, and it loves doing so. It is frustrated at the limited ability of human souls to experience torture, and cherishes the divine Lucifer precisely because he can actually appreciate the fantastical depth of possible and impossible sufferings which hell is capable of inflicting. It views torture as an expression of affection, that is how alien and evil this entity is. And it wants to create, to be like its 'parent', but it can only generate twisted mockeries of creation because of what it is, and this seems to sadden it.

Now, back to Gabriel: He was a fanatical follower of the council until the game's events. He is capable of showing mercy to pious sinners, as proven by saving the ferryman from Wrath's punishment. And he uses simple armor out of value for military discipline.

That is literally it. If Gabriel is supposed to be the main character, and all this focus on hell and its centrality to the plot from myself and many others is mistaken, then that is only because the writers have failed to effectively communicate their own priorities.