Okay, so I know that it's kind of frowned upon to bring up TV Tropes on this site, but recently a user there named Beast did a really great proposal for the version of Slender Man that appears in the ''Slender'' game series (''Slender: The Eight Pages'' and ''Slender: The Arrival''), and I really thought I should bring that discussion over here. And while I know it's also frowned upon to do this, I'm actually copying Beast's proposal because I thought it was so well-done. Here's the proposal, all credit goes to Beast.
This version of Slender Man has an aspect of his character that wasn't brought up previously that was overlooked when I tried to way in; the fact that he communicates and displays a deliberately malicious personality, much like his iteration in ''Windigo''.
This version is a character that haunted a park/forest but is much pretty unknown to the community. He's been responsible for disappearances for centuries but rarely left a body behind and has his eye(less) on the Matheson family on account of the grandmother of the family summoning him as a little girl. One day Slender Man goes after young Charlie Matheson Jr, terrorizing and mind raping him while his panicked family looks for him. We find out that Charles Sr. committed suicide as a result, and Charlie has since been turned into a perpetually suffering emaciated corpse like creature.
Two childhood friends, Carl Ross and Kate reunite as they intend to confront a childhood trauma from playing in the woods. Ross has since grown into a freelance reporter and is in particular is investigating Charlie's disappearance. Unfortunately he finds out the truth, and both he and Kate become aware of the Slender Man and how he can pretty much only be stopped if no one knows about him. Ross attempts a double suicide with Kate to bury the truth but Kate gets scared and Ross burns to death alone. At some point Kate is being stalked through the woods by Slender Man and when ultimately caught, Slender Man himself tells her that he has plans for her.
In the meantime Kate's mother died of mysterious circumstances, and Kate calls her other childhood friend Lauren to help sell her childhood home. Lauren arrives and finds Kate's home ransacked, and Kate has since turned into a ravenous Mind Raped slave of Slender Man that constantly attempts to rip her apart. Lauren spends the game ducking and dodging Slender Man and Kate (even encountering what's left of Charlie from time to time) throughout the forest as she begins to uncover clues as to what's happened, including those already uncovered by Ross. She also finds a tape of Slender Man attacking Kate in her house. Eventually Lauren finds the message to reach the radio tower where Ross burned himself to death and his message that Slender Man will die with all who know him. The forest catches fire as an increasingly ferocious Slender Man chases her. When Lauren reaches the tower, it itself catches fire, and Lauren jumps off the tower but while her camera dies, it's implied that Slender Man is keeping her alive because it's in his interests that she lives.
The extended ending reveals Lauren did survive and was taken to the Matheson farm where she is attacked by Kate.
In a seemingly non canon "secret level" that can be unlocked early in the game, where someone (presumably Lauren) will get a message from Charlie asking to find her, only to get a message from Slender Man that says he wants to play a game were he finds them in a twisted version of Kate's house. When inevitably caught, Slender Man will then immobilize their victim, burn them alive and kill them.
This Slender Man communicates with his victims through messages, especially taunting messages that imply a deliberately malicious personality. These messages are unlikely to pop up during a standard run of the game as they are circumstantial; he communicates to Kate when you're playing her level; he communicates and repeatedly taunts his victim in the secret level; and to the player when you try to glitch your way off the map.
His non verbal actions and behavior come off less like some mysterious presence he's usually portrayed as and more of a sadistic tormenting demon who likes to toy with his victims; especially when he goes after Charlie (who he slowly terrifies along with his parents), and again in the "secret level" (where he burns his victim alive as he slowly goes in for the kill). And given how some of his messages mentions "playing a game" with one of them, that may be the case. Also he doesn't just take people in this game, he Mind Rapes them into being wrecks (at best) physically disfigures and mutilates them, and leaves them in constant agony, which we see in Charlie and Kate, the former of which is constantly heard crying in his state (again, he was a small child when he was taken).