Hmmm, interesting. I wouldn't normally print vertically like that. Go flat and see if it prints the same way.

When I import the STL to SketchUp, I do notice that there are a number of "open" triangles, as well as many interior planes, usually at the mid-point within your 2x4s. Slic3r is pretty good at repairing those.

It's possible that Slic3r tried to generate support material for the top cross-beams, but that would have been as thick as the whole wall...

Weird. Print flat and show us your results.