Specifically it's the date shipped/received fields I need to be in my source fields column. As you can see by the next screenshot, they are in my define database.
The fields in your database are your Target fields. The columns of data in your csv file are your Source fields.
You've clicked "Don't import first record (contains field names)", but I don't see any text from the first row of text in the csv file in your dialog box.
I'd open that file with a text editor or word processor and check to see if the first row of text contains column names or not.
You might also click the >> button to inspect your actual data to see what column of data is aligned with what field.