I love the Alexius Comnenus scenario on that game 
. Its definitely more feasible to go with a Byzantine revival prior to 1204 (and probably prior to the reign of Manuel Comnenus) since after that the 'empire' would never really be an 'empire' again. However, I wouldn't rule out a Byzantine revival taking place, say, after the fall of the Latin kingdom, but after that point its very unlikely it would ever reach its former glory and be more than a small state based in and around the Aegean.
Well, a state covering between Syria and the Danube can be called properly an empire by medieval standards, and after all the
Romaioi were the heirs of the imperial tradition in the East. Since the death of Manuel Komnenos, the disintegration of the state became evident, although the underlying causes can be traced earlier. If the issue is the mere survival of a Byzantine state around the Aegean Sea, perhaps a fictional success of the rebelion in Asia Minor led by Alexios Philantropenos -the so called "Belisarius of the Palailogian era" who ended blinded by the emperor's henchmen- might be an interesting startpoint for a storyline. Arguably that goal sounds too modest when I created the Kingdom if Rus twice, defeated the Mongols, Turks and other enemies and made the Mediterranean a Roman Orthodox lake in CK
