(...) why are the heatsinks on the NF1 and the ASICMiner thumbs on the bottom?
That's due to the chip design. Most desktop CPUs are designed to dissipate heat through the packaging - so the packaging material for them is metal. But that's very expensive.
The cheapest chip package is plastic, which unfortunately isn't very good conductor of heat. To get around that they used the fact that usually the silicon crystal is first mounted on a metal base, and then the whole thing is covered in plastic (to put it a bit overly simplified). So they ended up with the metal bit that gets the most heat out underneath the chip.
In that case in order to move the heat away from the chip you need to channel it literally through the board towards the back of the board (using numerous "via"s or holes which itself are copper plated and usually during the soldering process get filled in with tin or whatever the soldering material). On the back a large copper plane acts as a heat sink. Or you can add an additional heat sink on top of it.
So if you look at it from a 3D prospective it looks like small heat pipes (the tin-filled vias) that connect the chip to the heatsink. Probably not the most efficient way but certainly cheap
