I am not an Inkscape user. However, I would guess that perhaps the files are a bit too complex.
Opening one of the files in Illustrator CS6 I find a great deal of unnecessary objects - which appear to be very large type glyphs (all that black in the image below) - in addition to at least 9 nested groups.
Once I delete all those unnecessary objects I'm left with the base art which appears to look good - or at least usable, still in several nested groups and clipping groups though.
Of course, the art appears to be upside down and flipped, but that's an easy fix.
It's entirely possible that all those type glyphs were related to some text at the bottom of the artwork and simply got distorted upon either the SVG being saved, or Illustrator opening the SVG file.
- Opening the same file in Illustrator CC2014 shows the same configuration with the exception of the Illustrator artboard being in a different location.