This is a very good question and one which the Early Church obviously never had to consider, although there does exist a traditional teaching to fall back upon. At sites and places of great pilgrimage, pilgrims who were unable to enter the church due to the size of the facility and/or sheer number or persons, were still said to have “participated” in Divine Services even though they were outside the confines of the church’s temple.
Therefore, if you are watching a live broadcast of Christmas or Paschal services from Moscow (whether outside the cathedral on big screens or within your own home) and the Patriarch blesses the people, then it seems to me that you may include yourself among those who are receiving that blessing. This, in my opinion, would also apply to internet or radio broadcasts.
On the other hand, if you have a cassette, VHS, of DVD recording of a past service that you like to listen to or watch on a day when you are unable to attend church, those blessings are not valid because there is no priest giving a blessing at that exact moment.
