I don't think Thanatos cheats, he has to have an overpowered piece of gear with a skill like "if incoming damage surpasses your remaining Hit Points, your HP is halved instead." Eventually his HP will be 1 (say, when he's shot in the neck), and then any incoming damage will never bring him fully to zero - just like Zeno's paradox on distance.
As for his identitity, my bet is that he's actually Luna's father: 1) You having the gem of doom was a secret almost no one knew about, yet Thanatos comes for you. Luna saw you get it - she even told you to hold on to it. 2) Luna first gives out the chip as a contest price because her father doesn't want it, yet when you go over to her home to play, she lends you a spare suit she has. Why does she have a spare? It's her father's - Luna knows who he is, and helps him. 3) Why do I say this? Think of the ambush Daliah invited you to be part of: Jeremy was killed by an ogre who appeared out of nowhere. Luna is a summoner. She summoned that ogre to help Thanatos, his father, get that gem of doom. 4) Now, motivation. What could drive a man to such extremes? Mr Hernandez said it: "I promised my wife I would do anything I could to care for Luna", or something along those lines. If he collects the gems, he becomes the CEO of Ulysses and can grant her anything. 5) Circling back to your point on skills: I don't think Thanatos is that skilled, but that he put in a lot of work via theatrics and what not (leaving those arrows sticking on his back) to build up this reputation, so when people see him their fear of him makes him lose. He even lets you and Daliah go so you spread tales about him. This is a game, it's all about pretending to be something you are not. Nova tells you she's got a reputation to keep, Jeremy gives his introduction a lot of importance, etc... Thanathos does the same, and that intimidation factor gives him an edge, a boost. Luna deceives you on 3 of the first 4 times you meet her ("you're dead", "I had a sister", "the voices..."), the last time her father is even in on it with practical effects to sell it. Extra point 1) Luna asks not to try the divination on her - maybe because you'd see a memory of her and Thanatos? Extra point 2) Thanatos eyes are red, like Luna's.