There are three move-order settings in warzone:
1) No-luck Cyclic: the move order is shown to all the players. The player who got last move on turn n, gets first move on turn n+1.
2) Cyclic: the move order works the same as with No-Luck Cyclic, but the move order is not revealed to you or other players. In this case, you have to figure out what the move order is, given the move orders you have seen over the past turns.
3) Random: the move order is not revealed to you or other players and is randomized each turn.
You can read more at https://www.warzone.com/wiki/Move_Order
Move order is only shown on games which are Cyclic No Luck, aka PureSkill.
No-Luck Cyclic is not Pure Skill. Pure Skill requires a game to have No-Luck Cyclic move order, 0% luck modifier and straight round rounding mode.
Edited 1/22/2020 15:46:59