Commerce Kickstart differs from the standard core installation profile, by having extra installation steps. These steps are illustrated in the offical Commerce installation docs - they ask questions about store features and whether or not to install the sample store data.
Installation via drush does indeed work, however it does NOT offer these extra-step choices to the user. Instead it assumes you want the sample store.
So installation via drush is straight-forward. Assuming you have downloaded and unpacked the distribution archive file, just
cd to the Drupal root, and run
drush site-install commerce_kickstart.
Take some time to review the options described by
drush help site-install. Most likely you will need to pass in a few more options, such as database credentials. A typical installation command will look something like this:
drush site-install commerce_kickstart --account-pass=admin --account-name=admin --db-url=mysql://root:pass@localhost/db_name --notify
Note that the Commerce Kickstart takes a lot more time than the standard core install profile. It sets up over 100 modules, several content/product types, and imports the sample store data.
drush site-install will tell you "This takes a few seconds...", but it took 10 minutes on my machine :-)