QFG1
Here, the thief is a new hero, so he isn't all that agile to begin with. Also, there really isn't much in the way of agility-related stuff in Spielberg other than what was seen in the original.
QFG2
In the vast desert city the thief finds himself in, there are plenty of rooftops to run on and jump from. Learning to traverse the rooftops on foot allows the thief to quickly access various parts of the city faster than the other classes - after all, even with the map, they still have to navigate the busy streets - and builds up both his endurance and his agility points. This gives him an edge in combat as well since he can perform wall flip-kicks and jump off of the occasional wall or solid object - but he can't do it too much at this point as he isn't agile enough.
QFG3
In the large Savannah city the thief now finds himself in, there are plenty of rooftops to climb and jump from, just as in QFG2 - except they are so high that climbing isn't the quickest option. Therefore, the thief must combine what he learned from his roof-traversing and heroic acts in QFG2 to swing from the many ropes connected between the buildings in addition to climbing and jumping from and off of the walls in order to quickly traverse the city vertically. Besides helping him train for the tribal rituals later in the game, it will help him in combat as the thief will be able to nimbly jump over many monsters and foes, depending on their height and what objects surround the hero when he fights.
QFG4
This is where it gets interesting. In spite of the lack of vertical space like there was in QFG3 and the almost complete lack of buildings to climb and jump across, the hero will still be surrounded by plenty of objects on which to jump off of and otherwise perform all the awesome tricks I described in the beginning of my post.
QFG5
I never really thought this far, but based on how I heard that thieving in QFG5 is a bit more involved than in the rest of the series, I imagine the thief would end up being like Ezio Auditore di Firenze!

So there are my thoughts on how the thief's abilities could be fleshed out more in a complete 3D remake of the Quest for Glory series. If anyone has any suggestions, comments, feedback, or criticism, please feel free to reply to this post!