That picture is misleading... Especially the counting part. You could go through all the numbers 2^256 across a lifetime if you wanted to with a computer that was fast enough. I think it would have to assume some kind of minimum period between the counts.

I don't believe it has anything to do with the total number of atoms or matter in the world. I'm pretty sure there are more than 2^256 atoms just on earth. Many times more in the universe.