If there is at least one file in the current directory whose name begins with wine, then wine* in the command expands to the list of files whose name begin with wine. If there is no such file, then
sudo apt-get remove --purge wine*
is executed. Arguments to apt-get install and apt-get remove are extended regular expressions, not shell wildcards; wine* means win followed by any number of e, and since this can match any part of the package name, this means any package whose name contains win as a substring. Plus, of course, any package that depends on these packages.
If you were using KDE, then you lost the kde-window-manager package. If not, you must have lost some other critical package. Maybe libmate-window-settings1 which is required by mate-control-center which is required by mate-desktop-environment-core whose loss would render most of the MATE packages superfluous. I checked Debian wheezy package names, Mint might have a different set, but you get the idea.
To remove just the packages whose names start with wine, use
sudo apt-get purge '^wine'
Check the list of packages carefully before confirming.
You may be more comfortable with Aptitude, which has a text mode full screen frontend.
sudo apt-get remove --purge wine *accidentally putting a space betweenwineand*? Because that would do it. – Alex McKenzie Jun 03 '14 at 20:16apt-get remove wine *would remove all packages whose name is a file in the current directory. In an empty directory, it would error out. – Gilles 'SO- stop being evil' Jun 03 '14 at 23:25apt-get remove wine *is equivalent toapt-get remove winein a few cases (bash or zsh with thenullgloboption). – Gilles 'SO- stop being evil' Jun 03 '14 at 23:58