I wouldn't call it interacting with the strategic level per se; to me what's important is the way in which the PCs interact with the game world. For example, if the party is trying to clear out a cave full of kobolds and one of the players suggests diverting a nearby river so that if flows into the cave and everything drowns, will the other players be on board or will they feel cheated because they didn't get to fight the kobolds? Does the game system reward them, punish them, or neither reward nor punish them for choosing to deal with the problem this way instead of entering the cave and fighting it out?