I ran into same problem and here was my solution to work around it. The problem seems to be in the new 3.6.0 version, so back out the new version and install the previous version.
gem uninstall mini_magick
gem install mini_magick -v 3.5.0
After installing 3.5.0 mini_magick gem, rerun the watir gem install. It should find the mini_magick gem already installed and skip over it and install the remaining gems successfully. Good luck.