I don't agree.They seems rather bored, and Anastasia has a mischievous expression at her face. The only one who seems over the point of staring to cry is Alexei. But maybe it's an optical delusion. I think it was summer and all people feel miserable dressed as they were in the middle of a heat wave.
As for the war, I think it lasted some time to begin, yet. When the WWI started, Anastasia had 13, and Alexei , 10. They didn't seem to have this age in the pic.
RealAnastasia.