Both heroes choose an option from the table, then compare in the combat phase. From what I can tell, this is instead of anything else they would do (ie, ranged attacks, movement, spells) apart from command abilities. There is a command ability to allow an unengaged unit to attack the enemy superhero, then that unit is immediately destroyed.
From what I can tell, there's no restriction on using the same action over and over again, and, while the article claims making your choice is some sort of tricky, tactical game of out-guessing your opponent, in reality I don't see any reason shy Archaon would ever choose anything other than "all out attack", which guarantees first strike, ensures nagash will never cast a spell, and while you might suffer a penalty to hit if nagash defends, it's not like there's any action that would be better to choose if predicting a defense.
The course of the battle outside of this table isn't described at all, and only comes up twice due to nagash calling in units for the command ability attack, but it's hard to envision the death army actually clearing all nearby chaos models to get close enough to use them that way, and between that and the chaos player making overtly bad choices from the table as the feeling of a battle report deliberately obfuscating how pointlessly lopsided and exploitable this scenario is.