Externica: So in short:
The game has no meaning at all? Thank goodness, it really felt like I was missing something very important.
First I thought, that the parents of Leah were all dead and that she lived in this big mansion all by herself.
Then I thought, it was all a dream because of the fire and this was a clue how everyone but Leah died. (I mean, the mansion is burning and all she does is going to bed?)
Then we heard about birdie and I thought it was some kind of bomber and Leah was either a scientist or a spy.
Those weird phone calls.
And in the end.. birdie was a bird...
I really didn't get that game and on the same hand, it scared me. Because I had no clue what was going on.
It could've had some intended meaning, but they refuse to say and leave it up to theory crafting. I like my really straightforward take on it.