But more in line with my point, LARPing actually starts to develop organically in very very good CRPGs where it ends up being beneficial to the player to act in a consistent manner within the framework of the game's universe. See Age of Decadence. This is a game that wants you to treat its world with logic and care. In this way, LARPing in a good CRPG is a completely different thing than LARPing in a bad CRPG. In a good CRPG like Age of Decadence, you end up playing a role organically, because the world makes sense and rewards realistic behavior. In a bad CRPG like Skyrim, you end up LARPing because the world is essentially a bland sandbox bereft of notable interaction or consequence, where imagination is literally necessary to create some sort of carrot on a stick to keep you holding W toward the horizon.
In your post you continuously confuse and interchange LARPing with immersion and role-playing. LARPing is a dysfunctional form of role-playing.
In P&P setting, the LARPer would be the annoying guy who keeps trying to tell the DM that he's a dwarf while the game is about space travel and he rolled a technician. He'll talk like a dwarf and refuse to attempt to reach the control panel, because his stats say he's tall, and he can't let a dwarf succeed at height-demanding tasks.
A LARPer is forced to comply to existing world rules, therefore he has to twist his worldview and mess with the gameworld to try and keep a barebones illusion of it his fantasy being validated by the gameworld.
In your chess example, a LARPer may decide that his King has claustrophobia, walk him out in the beginning of the game, and get checkmated. Though chess is really not an RPG, so using it as an example is not particularly relevant.
I believe that the most common cause of LARPing in CRPGs is the gameworld's inability to maintain cohesion in reaction to a variety of possible player choices, and/or not even providing the choices the player is looking for. The more the game world and mechanics fall apart, the more it is likely to be LARPed. Hence, Bethesda fans.