Paul Farquhar
Legend
It's perhaps a good idea to actually read up on the gods in the campaign setting you are using...
I am speaking strictly mechanically. If you want to reskin another cleric domain as a cleric of war, go ahead.
Speaking only mechanically, all clerics share the same chassis. That can't be used as a point of differentiation between domains. So looking at the mechanics of the domain that was published, the specifics of what the war domain is meant to represent is personal excellence in battle. Again, this is irregardless of what the setting or other fluff describe, the mechanical expression in the rules of the War Domain is this.
So, if you want to know if an Order cleric can replace a War cleric mechanically, the question is are they a better personal warrior under the rules. Which has a clear answer of no. That's the scope of my answer.
In a different scope, such as going with the definition of a War cleric for a specific deity or setting, the answer can easily be yes. I don't think the mechanics do a good job of describing "War", since to me "War" is done with large numbers of combatants per side and the mechanics of the war domain don't fit that.
Does that answer sufficiently?
Tempest is the main "melee" domain and in that sense a "replacement" for war.
I still don't like how you unequivocally conclude Order can't replace War.
I would say the Order level 1 ability does a much better job at warpriesting than what the actual War domain grants, assuming you tweak it to "self" instead of "ally".
In fact, we just had a discussion on the wonkiness of War Priest! The Order L1 ability (given self) is precisely what the doctor ordered!