Ah, that's interesting. Speaking from personal experience (and as an atheist, who happened to grow up in a religious household), I think many atheists are too quick to dismiss the value of rituals/prayers/meditations. As you pointed out, there can be value even if the deity to whom the prayer is offered doesn't exist or isn't listening.

For example, growing up my family began and ended each meal with a prayer of, essentially, thanksgiving, with a few other requests thrown in ("keep us safe", etc.) This delimited the meal time: we were there for the duration, we all started eating together and there was no leaving before the meal had ended. I don't remember the prayer any more but I do have fond memories of family dinners, the unity and connection we all experienced during that time and the spirited conversations they featured. Prayers of thanksgiving also center the experience of eating in one of gratitude.