Motzei Shabbos, the eve of December 25, is Nittel Nacht, a gentile holiday.
On this day there is an extra abundance of impurity and a stronghold of Kelipa. For this reason, the Jews throughout the generations took various customs upon themselves which are followed until this day, in order to diminish the spiritual power of the impurity.
It is the custom of many Jewish communities to refrain from learning Torah on this night so as not to add strength to the forces of impurity – kelipa.
This is the Chabad custom as well, and it is said that the Rebbe Rashab was not happy with those students who ignored this custom and continued with their studies as usual.
The custom to avoid learning begins from the night of the Eve of the 25th of December until midnight. Starting from midnight, one may resume learning Torah, and there are no longer any restrictions.
Many have the custom to play chess on the night of Nittel.

that picture wasn’t taken on nittel
This picture was NOT taken on Nittle nacht. Rather, it was taken some time when the frierdiker rebbe was sick (lo oleinu), so the doctors told him it’s good for his health to play chess, so the rebbe as a caring son-in-law took it on himself to play with him.
What would be the reason behind the custom to specifically play chess? When did it start and by who? Did the Rashab and the rebbes preceding him also play chess on nittel nacht? Was this something the Rebbe and the Rayatz did every year or was this a one time thing that happened to be photographed? If the Rebbe played chess on Nittel Nacht who did he play against?
The idea of chess is that since you are not filling your mind with Torah you should at least fill it with something you need brains for so that it’s not just sitting empty waiting for shtussim to fill it. chess sharpens the mind. Another minhag is to sew buttons – same idea, use your time to do something productive.
There’s no mitzva to play chess specifically. If you want to go in mivtzoyim or spring clean your home that’s fine too.
Because some other groups played cards, so in reaction, groups like Chabad said not to waste your time with cards, but to use your mind.