Maarten D. de Jong
So, no, it's not a perfect information game, but luck does not play that big a role.
It is not a perfect information game because of the stack of order chits which is formed, thus hiding which chits have been played; the fact that dice are thrown has very little to do with it. A game can be perfect information yet contain random elements!
The dice... Well, they have an influence in that they prevent players from building up impenetrable strongholds which are nearly impossible to take over. But it is not correct to attribute loss to them entirely: once every player has refilled their hand the action selection is very much a controlled choice. Replacing one die with a joker could alleviate some of the worst of the remaining capriciousness; the favoured solution is the open selection from n + 1 previously drawn groups of cubes where n = number of players. That variant can be found here in the subforum. But in order to keep the game moving, some randomness in the cube replenishment appears necessary.