The error message you get is;
Status: Failure - I/O Error: SSO Failed: Native SSPI library not loaded. Check the java.library.path system property.
Which is nicely displayed at the bottom of the "New/ Select Database Connect" dialog when you're trying to connect to your SQL Server instance;
|Oracle SQL Developer: Windows Authentication Error|
This .dll is included in the installation (which includes the JRE and the SQL Server plugin). If you do a search in the directory;
|SQL Developer Install Directory|
Copying to to the root directory will allow the application to work without having to install anything on the machine it's running on (as opposed to altering the path or copying to file to somewhere else that's already on the path).