First of all, any game can be a children's game when correctly matched to the child.
My daughter's favorite game is Machinarium. She memorized the demo when she was 3, and kept wanting to play it and to play more than what was available in the demo. So, I had to buy it.
It's now about 2 years later, and we've beaten the game more than 10 times. She keeps getting better at it and needs less of my help with the harder puzzles and the action parts.
She also likes Little Wheel and can play it all by herself. Although, she prefers to have me help her with the timing puzzle with that involves lining up the wires in 3 asynchronously rotating dials.
Then there are the games at pbskids.org
, which she likes for their simplicity.
If I'm playing a game on my PC, she usually wants to watch or to know which buttons she can press to help me. However, she will want me to mute the music when it is tense or dark. At first, she even disliked the robot announcement voice that comes from the radio in Machinarium and would take off her headphones whenever she heard it. She now tolerates it.
Similarly, my younger brother was more sensitive to music more than I was when we were kids. We grew up with a NES and played almost anything we could get our hands on. However, the dungeon music in the Legend of Zelda gave him nightmares, so I had to play them.
You should, however, reconsider your question about games for children 4-10 years old. For young, growing children, each year can be like a lifetime. Also, more than one new skill is learned during each year.
If you want to make a game a game for a specific age range of children, keep the range small (a range of 1-2 years for example). Also, the younger the child is the more easily that child will be easily frustrated, distracted, and impatient.