This option is indeed gone. The button was used to toggle the isReborn property of a player on or off. But this property is not in the game anymore because its functionality has been replaced by a better implementation.
The first function of the isReborn property was required in the implementation of the reborn civs. Many game mechanics used to be tied to the player ID (often referred to as "slot") The reborn civs shared the same slot with another civ. For example the Aztecs and Mexico shared the same slot. The isReborn property was required for the game to know which civilization was using the slot. The new implementation decoupled the mechanics from the player ID and these are now connected to the civilization itself. So the isReborn property is not necessary anymore.
The second function of the isReborn property was to switch between the normal stability map and the alternative stability map. For example the Phoenician core move to Carthage when the city of Carthage is settled. The switching of stability maps has been incorporated in a new mechanic called "periods". The isReborn property only allowed for 2 periods (the normal one and one when the isReborn property is set to on), but the new feature allows more than 2 periods. A civ could have an alternative stability map for each period. For example all dynasties of China could be represented with their own period, each with a stability map that is accurate for that dynasty, instead of having 1 or 2 maps that have to cover all in one. (Currently now new periods have been implemented yet. Only the secondary maps that were already included with the reborn function have been converted to work with the period function) These periods can also be used to changed the modifiers of a civ, but IIRC they are currently only used to change the stability maps.
The WB will be updated so it can work with the new periods mechanic. But it is not able to yet.
