This is the way the Eastern Orthodox cross themselves. Priests and laity. Crossing yourself is a form of prayer, a physical prayer that can be accompanied by words, or not.
The gesture priests do is part of their ministerial priesthood, in which Christ blesses through them, who are living icons.
The gesture every christian does on themself is part of the universal priesthood of believers, in which the christian, being baptized in the death and resurrection of Christ, is a part of his body, is assimilated to him, and therefore through Christ has now a direct access to God, through prayer and intercession.
I've seen some lay christians bless the food before eating with the three fingers instead of the IC XC sign, I mean why not.
The roman catholics, copts and other christians who cross themselves,, they do it left shoulder to right shoulder and not right to left, that's something only eastern orthodox do.