What is the ruling on opening an internet café while adhering to Sharia regulations, or limiting it to computer games, and is it considered a sin if customers do not pray, and is it sufficient to exempt them from payment at prayer times to clear one's conscience?

The owner of the internet cafe must close the shop at the time of prayer and go to perform congregational prayer in the mosque, because congregational prayer in the mosque is an individual obligation (fard ayn). It is not permissible for him to remain silent about someone who misses the prayer time while in his shop, as that constitutes remaining silent about evil (munkar) and cooperating in sin and ithm.