The internship is available through the Gate Theatre, not a study abroad program, though my university did set up my particular internship as they have a long standing relationship with The Gate. As you can see from the link it is a full time internship, but if you mention that you're a student, you may be able to work out different hours (longer hours on days you don't have classes, etc.)
Really, it's a great opportunity and unless the theatre has moved and undergone MASSIVE changes since 2006, it's a small operation and if you make an appointment to talk to them I'm sure they'll interview you. The current general manager, Undine, was there as an office staffer when I was there and she's nice.
It's always worth a shot to send in your CV and cover letter and see if they get back to you.