There are some new network gaming shops being opened, where there are lots of computers, and in the computers they offer children to play many different games.They charges you per hour to play the games. I wanted to ask if this sort of playing is gambling or not?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Gambling is when the winner takes the money from the loser. So if this game is like this, it is absolutely forbidden. However, if these games are free from gambling then they are of two kinds:

1) If these games include some prohibitions like music or pornographic pictures and so forth, it is not permissible to play them or rent them as this is helping in sin.

2) If these games are free from these kinds of prohibitions, then it is permissible to play them without being extravagant and wasting time, and it is permissible to rent them. 

Allaah Knows best.