Two games, two Athenian victories.
The first special rule is ambiguous. If by terrain hex it means the broken ground hexes, then why don't we say what we mean? Second, both the first comment below and the map above suggest that the left and centre sections of the battlefield in the rule are from the Spartan point of view, but we took this to mean from the Athenian perspective. In other words, all three broken ground hexes are included. From a logical standpoint, surely this makes more sense - why exclude one of the three and also the one clear hex behind the Spartan ramparts? Also, is only one hex included in any game or can different Athenian units occupy any one of the three? The use of the word "one" in the seventh word in the rule raises an ambiguity. I guess the intention is to count each and every Athenian unit running amok behind the Spartan lines regardless of which broken-terrain hexes they may have passed through, but the rule as written is as clear as mud.
A further thought, if a light or auxilia unit starts a turn on the hex between the hill, the broken ground and the sea and moves two hexes into the clear hex between the broken ground and the ramparts why would this not earn the victory banner at the start of the next turn? The rule as written states that it has to start a turn in the broken ground, but logically why? Furthermore, historically, the Athenian outflanking force climbed a cliff, which I presume is what the broken-ground hexes are simulating. If they are contained on the cliff surely they pose no threat. Personally, I would word the rule to award the banner only after a unit breaks out into the clear terrain behind the ramparts, so something along the lines of "Each Athenian unit, which at the start of the Athenian player's turn occupies a clear hex behind the Spartan ramparts having got there by crossing the broken ground in the gap between the impassable hills and the sea, will gain the Athenian player one Victory Banner. The Victory Banner is retained as long as the unit remains in a clear hex between the ramparts and the Spartan baseline inclusive and is not eliminated." I would also remove the two broken-ground tiles beyond the one hex of the chokepoint.