Sorry, what? What would cause more debris to be on the side that collapses quicker? What horizontal force is being applied?
Gravity, of course. Mostly, it would be pulling the debris downward in a straight line. But, because the lower floors were not getting out of the way at the same speed , the debris would pile up a bit, then start to move laterally. The perimeter columns, deprived of their lateral supports, would offer less resistance than the undamaged floors below, and would yield suddenly, allowing gravity to pull loose bebris off over the side of the pile, like the sand piling up on top of a solid block of wood.
Again, this would require a horizontal force.
If parts of the building collapse later than others they will be subject to long column type failures which will not favour one direction over others, except in the direction of the force on them, due to gravity.
Again, compparing the debris to sand poured onto a wooden block, if there is any object resting against the block so that the top of it rises above the edge of the block, less sand will be able to fall off that edge and will, instead, tend to run off the other edges. In the towers, the columns that failed at a lower level would allow more of the pile of debris to slide off in that direction, so that the surplus which was acting against the least damaged face, but not able to move downward agfainst the resistance of the lower floors, would tend to slump into the more damaged areas.
Although the collapse may be assymettric the debris is subject to very little horizontal force due to your 'incline'. This would be more significant if that 'incline' itself was not acellerating downward.
But the incline was accelerating downward at far less than g, while the debris could only accelerate at exactly g. Thus, it has to go somewhere other than straight down.
However we also have to take into account the core which itself lagged the perimeter in collapsing. This would separate the sides of the towers slowing any lateral movement of debris and, as I believe Oystein or Lefty pointed out, would then be a guide that would allow the sides to collapse largely independant of each other.
The core is a bit of a sticky wicket here. It did moderate the flow of loose debris so that it did not all move toward the more advanced front.
I can see how collapse would have arrested in a more conventionally-designed building.
But that is the fly in the oinment. It wasn't conventional.