All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the game of domino includes playing with dice, then it is forbidden, but if it does not include playing with dice, then in principle it is permissible provided that the game is not about money and provided that it does not lead to missing a religious obligation or committing a forbidden matter; for more benefit, please refer to Fatwa 91109.
As regards those people who play in the mosque in the manner which you mentioned, then no doubt it is forbidden because it leads to missing the Fajr prayer in congregation and the Prophet disliked talking in the night after ‘Ishaa' prayer because this leads to missing the Fajr prayer and the night prayer. Abu Barzah said: "The Prophet disliked sleeping before the ‘Isha prayer and speaking after it.” [Abu Daawood]
In principle, the mosque should be free from playing as the Prophet said about mosques: ''It is build for the remembrance of Allaah, prayer and the recitation of the Quran.’’ [Muslim]
Moreover, the amenities of the mosque should be used for matters of worship and matters related to it. Therefore, those people should be advised and you should clarify to them that they are wrong and point out to them that they will be questioned (before Allaah on the Day of Judgment) about the time which they spend playing. Ibn Mas’ood narrated that the Prophet said: ''The feet of a servant will not move on the Day of Judgment until he is questioned about five things: his life how he spent it, his youth how he used it up, his wealth from where he earned it, and where he spent it, and about his knowledge how he acted upon it.” [At-Tirmithi]
However, one should be wise when advising those people; the fact that they threaten to break away from the mosque means that they do not know the value of frequenting the mosque (and worshipping Allaah in it) and they do not know the seriousness of the situation they are in.
Allaah Knows best.