Find all directories (type d) that do not start with a dot (!) and do not have a name that starts with a dot (-name ".*"), then randomly select one of them (awk 'NR==int(rand()*NR+1){print; exit}') and delete it and all its contents (-exec rm -rf {} \;).
find . -type d ! -name ".*" | awk 'NR==int(rand()*NR+1){print; exit}' -exec rm -rf {} \;