This is, admittedly, a complete guess based on nothing but three words, but whatever, not like I’ve got anything better to do.
There’s an odd moment in the gameplay trailer where Escharum says without challenge he grows “weary, lost, alone”. “Lost”, perhaps, but “weary” and especially “alone” seem like strange words for a soldier lamenting a lack of action. “restless” and “bored” sound much more fitting for me. He also looks noticeably melancholy when he says this; he breaks off eye-contact and looks off into the distance and all the anger goes from his voice. Even other Brute characters, violent though they are, don’t seem THIS dependent on fighting; they respect martial prowess, of course, but seem more hedonistic and impulsive than strictly addicts to the act of killing.
He also makes it pretty clear that he just wants to die and that “this is his last battle”; his thoughts are more about being a martyr of sorts and his legacy than any immediate concerns about his own life.
And on a more general level, I think 343 are going in the direction of a more humanized villain; even at face value, Escharum at least seems to have vague notions of honour and respect for John which is probably more than any other brute we’ve seen before.
So, with all that taken onboard, here’s my stab at what his character’s about. Escharum is, as he states, fundamentally weary, lost, and alone. He’s able to identify these feelings, but can’t even begin to try fixing them; so, as he says, he fills the hole with killing, mayhem, and warfare. It’s like stress eating, just…gorier. But it’s only ever a distraction and is short-term at best. So he focuses on “martyring” himself and building a “legacy” of killing Chief, which he thinks will somehow fix himself; he’ll be happy and content once he finally kills the legendary demon, right? And if he dies in the attempt…well, so what? On at least a subconscious level, Escharus doesn’t care about himself in the slightest, and probably outright hates himself for being so emotionally vulnerable. Better to die than to be so weak.
And I don’t really have any evidence for this at all, but I can see Atroix actually being LESS sympathetic in Infinite; as this charismatic leech who latches onto those will low self-esteem and makes them die and fight for him. You can make clear parallels to cult leaders and radicalization if you want to go all English lit on us. Maybe as the game develops we’ll see Escharum’s facade crack more and more. I don’t expect a full heel-face turn- I think he’s too far gone for that- but I think as he’s dying we’ll feel nothing but pity for him, and perhaps a note or two of redemption.
Any of this true? Probably not, he’ll just be a brute desperate to fight John and that’ll be the extent of his entire character, but whatever, it’s fun to speculate.