I gave a somewhat detailed look to GravityWave save and IMHO there is definitely a bug in here....
First things first: This is a game with 18 civs, all of them alive ATM besides Babylon, that was player #6 ( you can check this easily ). The human player is Bizantium, that is player #4. The players before #4 already played ( including England, the master to be of America )....
When the human finishes its turn in 1714, the game goes to player #5 ( Russia ), skips #6 ( Babylon ) because it is dead, passes to #7 ( Egypt ) and so on ( I had checked friendly and enemy moves to keep track of all ).... all is normal until the ( BUG ) warning that England founded Dover and the diplo window of Lincoln ( that gets to be player #6 instead of Hammurabi of Babylon ), followed by the Rifling tech window....
After that the game shows Egypt, ... , moving the units again and it is in this phase that the flying pikeman attacks the city and the korean Speedy Gonzalez gets to that forest. This can be checked by the Event log, that shows the mongol pike attacking in 1716, before the human move , a thing that shouldn't happen because Mongolia is suposed to play after Bizantium by the player order.
Seeing this I decided to mark some units of various civs to check for double movement. All of the tested civs showed it, except Russia ( player #5 )....
The conclusion I can take from this ( that will require obviously code check ) is that the game started the year 1716 playing with the newlyfounded colony ( player #6 ) instead of starting with player #0 ( England ) and that continued the order until player #17, resuming to #0,1... until the player #4 , the human, giving a effective 2 turn period in the IBT to all the AI except for poor Russia