Tonight, 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.


Starting 4:30? Or 5?
The time for Brooklyn,NY starts at 4:30
From your post It may be assumed that this photo you share, of the Rebbe & previous Rebbe playing chess. Is actually a photo from Nitul Night (Dec 25 or Jan 6).
It isnt from that night, rather It is a photo in Perchtoldsdorf, Austria, around 1937, for his health, at a resort where fresh air and relaxation were encouraged at a health spa for his medical recuperation, the Rebbe would be there assisting.
Historically, xmas eve was a dangerous time for Jewish communities in Europe.
is as stated in the article, based on Hayom Yom, 17 Teves. Your reasons are correct on a more surface level.
of Rebbe and Previous Rebbe playing chess is unrelated to Nittel Nacht. It was taken in Austria at a health spa where they advised the Frirdiker Rebbe to engage in such activities to promote his health