This is one of the scariest games I've played. I would not recommend it for children who are easily emotionally moved by games. The game doesn't really have anything inappropriate about it. Some people here say Slenderman kills you, but when Slenderman shows up, if you look at him, your screen starts going fuzzy at a faster rate depending on how close he is to you and you eventually lose if your screen reaches full static. He is not supposed to kill you in this, the idea is that he drives you insane and the level of static is an indication of how "insane" you are. It is a very creepy game because he teleports around and always teleports to a position out of sight and you look at him which starts the "going insane" part.
The myth behind "slenderman" is a little misleading. Yes, the idea is he kidnaps kids. It was something they came up with on some forums one day when they were holding a contest to fake "paranormal" photographs. One guy came up with the idea of "slenderman" and started editing in a very tall man wearing a suit who seems to either have a fully white head or wears a full white hood. People really liked this idea.
It is probably disturbing to some degree to talk to children about kidnapping or otherwise, but any responsible parent will teach them these are real threats you face in the world as well. We told children fairy tales about witches in candy houses who bake children and eat them so I'm not sure Slenderman is any worse of a myth than has been told to children for centuries. These fairy tales have served to both keep children safe by creating ways for them to understand adult dangers in a censored context (I.E. if you don't want to tell your children about risk of child predators and what that specifically means, you tell them about witches that eat kids and to, therefore, stay away from people you don't know).
Nevertheless, this game is extremely scary for me and I'm 29. There are other games I wouldn't let children touch that some parents wouldn't hesitate on but would be fine with a late elementary school/jr. high child playing this.