Technically nothing in the strictest definition of dictator, rather than its more colloquial uses, states that a dictator can’t care for his people or state. It just means that they either took or were given near absolute power over the government. This actually happens occasionally usually after a period of unrest. Where one person does win control and then uses their authority to establish a more legalistic government.
And also technically a military position can be a political one. The most obvious is historical shogun. Which was really just supposed to be the position that handles the emperors armies. Only it became more politically powerful than the emperor for awhile.
But anyway, if we consider Noxus a kingdom and there is no planned exit (like a term limit) for Swain’s political life, then Swain is a triarch. It’s like a monarch but there are three of them. I do not know of any triarchs historically. Though there is a few diarchs I’m aware of (rule of 2).
If we don’t consider Noxus a kingdom, more an empire. Then dictator would be the root we’d have to use. Now dict means to say which implies the absolute power where whatever the dictator says is law. This is different, the three leaders need to agree to enact policy. Triumvirate seems close but that was technically never a political position, it was just an alliance between three people who held various different government offices.
I’d go with something like concordator or concordor. Where concordare is the Latin “to agree” then slap an ator at the end to make it a noun. Of course, concordator sounds a bit silly. So if you don’t like it then Trifarix or whatever term Riot game has just as much legitimacy