First of all, get_node accepts a filesystem-like path, and scenes, after they are instanced, are just nodes somewhere in the tree.
This means that you can just do get_node("../../") to get the parent of the parent node.
But… there is a slight trick. The root node is /root, and it has the currently-running scene inside it, which means that you can use /root/Game to get to the node you want.
Oh thanks for the quick and detailed reply! I should have know it from a carefully read of documentation am examples.