Hey - I feel like a complete idiot for having to ask this here, but other people seem to be able to see a more detailed replay than the summary replay you see at the end of the game (that shows the whole world and all the cites). How do you access this? Thanks!

They do???

I wish...unfortunatly, no :(

There's currently no mechanism in the game that'll record your moves to replay it back at a later time (ala WCIII).