Why play "Questions" in a movie about existentialism?

In the movie "Rosencrantz and Guildenstern are Dead", the two characters play a game of Questions. This is because existentialism, I believe, is based upon asking questions. Questions like "why am I here?" which lead to deeper questions that lead to existentialism's conclusion that we can only prove so much of our existence to ourselves, and that beyond that there is nothing more. In the movie, Rosencrantz and Guildenstern start realizing that they don't remember their existence at all before the messenger came for them. They kept asking more questions, and came to realize that they themselves don't even know which one of them is Rosencrantz and which one is Guildenstern. I think that their game of Questions was included in the movie for the afore stated reasons, and because it spurred their discoveries about their existence and helped with their thought progression drastically in only one scene. It also shows the thought process put into questioning everything in existence, even ourselves, in order to try and find the right answers.