There are a few reasons brought down for nittel nacht.
The Korban Netanel says it’s a form of aveilus.
The Chasam Sofer rejects the opinion of aveilus, and say if that were the case, we’d be allowed to learn hilchos aveilus. It also would last the entire night, not just the first half. Instead, he says that the Christians would go to church at midnight for services. If they were running to pray and the Jews were sleeping, it would look bad for Jews. However, if the Jews got up at midnight, it would look like they were copying the Christians. So they instituted a rule not to learn the first half, but to stay awake doing other things. At midnight, they would begin learning.
The Sefer Kedushat Tziyon says it’s to teach us a lesson. Jesus was a student of R’ Yehoshua ben Perachya. Before he turned bad, he was an accomplished and learned talmud chacham. He’s an example of the mishna in Avos, that says Torah learning, while important, is not the primary goal – actions are (living the Torah, not just learning it.) Therefore, on this night, we suspend learning to practice the actions.
In any case, most of these reasons don’t apply anymore. Only the last reason does, and playing cards or chess is certainly not the actions that the mishna in Avos refers to.
The Chazon Ish criticized those who held of nittel, and made sure to learn extra that night. The Steipler learned as well, and even told others not to let him know when nittel was, so he wouldn’t be distracted from his learning.