According to Jan Doggen's answer I found the solution in another StackOverflow thread, which can be found here: EWS: Access shared calendars
The answer from Seph was in Visual Basic, but it can be easily converted to C#:
using Microsoft.Exchange.WebServices.Data;
DateTime startTime = new DateTime(2013, 1, 1);
DateTime endTime = new DateTime(2013, 12, 31);
var cal = new FolderId(WellKnownFolderName.Calendar, new Mailbox("other user's email"));
var calendarView = new CalendarView(startTime.Date, endTime.Date.AddDays(1));
foreach (var appointmentItem in service.FindAppointments(cal, calendarView))
{
Console.WriteLine(appointmentItem.Subject);
}