Free fall: That means with no retarding forces, which couldn't have been the case. 'Effectively Free Fall' might be a reasonable phrase and this would have taken place when the pillars of the ground floor gave way. It would need to have been either the weakest layer of pillars or the layer with the biggest load - so I assume it would be the ground floor that gave way. The whole of the rest of the building would have fallen by, say 3m, giving it a downward speed of about 7m/s (round figure). The impulsive load on the next supporting layer would have been more than the static load which broke the first layer of pillars so the next layer would probably have collapsed without slowing the fall by much. Then the building would have fallen a further 3m, accelerating further until the next impact. Less mass now, of course, because two floors were on the ground but more speed, so enough to break the next layer of pillars.
For the whole building to collapse, all that would be necessary is for the remaining sections to have reached a high enough speed so that bringing mass mass to a halt would involve enough force to break each successive layer of pillars.
The only 'mystery' in this scenario is how any structural engineer would not have specified dimensions and materials for the lowest level to support (with loads to spare) the whole of the building at all stages of construction. I would look for conspiracy (corruption) here. There is a lot of money to be made by anyone unscrupulous enough to use lower specified construction materials in a big project and you only need to pay off any inspectors or potential whistle blowers. Or it is always possible that some incompetent Engineer is used, who got his post through nepotism or other corruption. Most times, you get away with it but there are regular reports of buildings spontaneously collapsing in different parts of the world.
It is notable that it doesn't tend to happen in Europe or the US. I wonder why that would be?
In the UK, building regulations specify that even a single storey building must have foundations which are suitable to take more floors, just in case someone might want to extend upwards. That's an awful lot more concrete than absolutely necessary, taken over the whole country - but we can sleep easy in our beds as a result.