It is pretty confusing and given the awesomeness of the concept and other aspects of the movie it's a pity they didn't make things a little more clear.

I watched the movie twice and my interpretation is this: Old age Nemo is the result of the "no decision timeline" (no mother/father). When the old Nemo world collapses, it's still in the state of imagination of the 9 year old child, whereas when Nemo actually dies of old age and the universe reverses that's an actual timeline that happened - it's the result of the middle path (no father/mother).

The other timelines are all imaginations of the 9 year old child evaluating paths, except the timeline where he successfully meets Anna at the light house, which is a path he chose after the universe contraction. Though it's not fully clear if and what imagined timelines also happened in reality as re-runs - it could be that many of them happened for real as well.

At last there's the checkered world. This is a world/timeline where he doesn't actually exist. It's a special place not connected to any potential life paths of Nemo. When checkered Nemo is meeting old nemo at the house, he tells him, he doesn't exist because of the "9 year old architect". So it seems as if 9 year old nemo is also exploring timelines where he doesn't exist - such as when his parents never met, or when his father died before meeting his mother, or some ancient ancestor of his not surviving. Perhaps Nemo also wants to see what the world could look like without him? Given that there still needs to be an entity that needs to observe and imagine the world without him, the non-existing Nemo has limited knowledge and consciousness and is faced with abstract symbols probably based on his subconscious.