I was today years old when I learned LitRPG was even a thing that existed. How do they work? Do you have to do the game part?
No there is no game. The author is creating the system, as background, that governs certain aspects of the setting in the novels.
It's just a premise which uses the conventions of RPGs with science-fiction and fantasy novels.
In this case, the main character is transported to a world which has a lot of magic, and his personal system for organizing the magic he obtains functions similar to a role playing game. It informs him of him gaining experience points, levels, the function of his abilities like rules, the upgrades for such abilities, magic items, etc.. And as the characters grow in experience, and therefore levels and abilities, they seek out more challenging monsters to fight.
It's odd at first but once you get used to it, it's fun. Also the authors voice is somewhat silly, sarcastic, and lyrical.
Example:
"Jason squinted at the translucent interface hovering before him, his mind racing through the complex calculations. His 'Shadow Magic' skill was nearing level 10, granting him the ability to create a more substantial, shadowy doppelganger, but the mana cost was significant. He had to choose carefully; use it now to ambush the approaching pack of Dire Wolves, or save it for the inevitable boss fight lurking deeper within the dungeon."
From a
review I read of the books, "HE WHO FIGHTS WITH MONSTERS by Shirtaloon is the archetypal LitRPG story. It is the story of a geeky young man being transported who dies in a sort of accident and gets deposited inside a fantasy world that operates on the rules of a tabletop RPG. From there, he begins an extended campaign to level up his abilities, accumulate treasure, and stick it to every authority figure while making pop culture references that his fantasy companions are deeply confused by. That description will more or less tell you if you are the target audience of HWFWM or not."