Is there a trick to deploying Commerce Kickstart 2
Missing display/designs/CSS rules are typically a symptom of missing stylesheets or other CSS style rules. If you browse to your login page, Drupal reports many errors about not being able to create files. 

 

It looks like your intuitions are likely correct; the server is probably having trouble writing aggregated CSS files to the files dir. Try turning off CSS/JS aggregation to confirm this. If that fixes it, check ownership of the files dir/subdir to make sure it's the same owner as the web server process.