Firstly: 

The ruling on opening a shop to rent electronic games is based on the ruling on the games themselves. In the answer to question no. 2898 we explained the ruling, and stated that if these games are free of haraam things, then they are permissible according to sharee’ah. So there is nothing wrong with renting them to children, if they do not contain any of these haraam things, such as images of naked women, games involving witchcraft and music, and so on. The owner of the shop must choose games that are free of haraam things. 

Secondly: 

We have discussed the prohibition on chess and dice in the answers to questions no. 22305 and 14095. 

As for the wisdom behind the prohibition on these two games, Shaykh Ibn Baaz (may Allaah have mercy on him) said: 

The ruling on playing with these things is that it is forbidden, because they are tools of idleness that keep one from remembering Allaah and praying. This is well known to the scholars, because they distract and keep one from doing good. They also lead to competition and may lead to much evil between the players, and may distract them from what Allaah has enjoined. End quote. 

Fataawa Ibn Baaz (8/98). 

Ibn al-Qayyim (may Allaah have mercy on him) said: 

If the one who plays dice is disobeying Allaah and His Messenger, even though the evil that results from that is little, then how can the one who plays chess not be disobeying Allaah and His Messenger, when the evil that results from it is greater, and it keeps the players from that which Allaah and His Messenger love, and takes hold of the player’s mind, and distracts him mentally and physically, and wastes his time, and dabbling a little in it leads one to become more involved in it, just as drinking a little wine leads to drinking a lot, and people are more keen to play it for prizes than they are to play it for no prizes.  If there were no bad consequences involved in playing it other than it being a means to consume haraam wealth by gambling, it would be forbidden in sharee’ah, so how about when the evils that result from simply playing mean that it is haraam? 

How can one think that sharee’ah would permit that which distracts one so much from one’s religious and worldly interests, and generates enmity and resentment between the players, and a little of it leads to a lot, and affects the mind and reason as intoxicants do, if not more so? Hence the player becomes more devoted to it than the wine drinker to his wine, or more so, because he does not feel shy or afraid as the wine drinker does, and both of them are akin to the one who is devoted to idols. End quote. 

Al-Furoosiyyah (p. 312).