It's not just how much surface area, but, crucially, the surface area in contact with other molecules. Bear in mind that we are looking especially at van der Waals' forces here (or London dispersion forces, or instantaneous dipole forces, or whatever other name you have for them).
If you have a lot of long chain molecule together, almost all of their surface area is very near the next molecule. Examine these sausages. See how almost their entire length on the left and right side of each sausage is in contact with the next sausage. Going back to molecules, this represents a large surface over which the intermolecular forces can act.
On the other hand, branched molecules do not fit as tightly together. See this image (no pun intended)
Extra branches on the molecules mean that they do not stack as well, so for a given molecule, there is less surface area of that molecule in close contact with another molecule (therefore weaker van der Waals).