The same reasons that playing in VR is better than on a monitor. But then one would question why this is better than VR. If all the players are physically separ

The same reasons that playing in VR is better than on a monitor. But then one would question why this is better than VR. If all the players are physically separate and movement of physical pieces is limited (because all the opponent pieces are now virtual) you lose much of the benefit of AR. This device is really best suited for people playing together in person (with online play a nice alternative, but not a primary target). As such I think a better example of the sort of hidden state it would work well with is Stratego. In that game the full board is visible to everyone but the identity of the individual playing pieces are not. There are many other things you could do with hidden state, like show the stats of all your pieces floating above them, but not those of the opponents. Or show terrain of the board where your pieces have visited to you, but not to your opponents (who have to guess by your motions). It doesn't need to be completely hidden - partial knowledge or fog-of-war can make for interesting game dynamics as well.