Why doesn't the following stored procedure compile with MySQL Workbench version 6.3.?
You're just missing the keyword THEN. Read more about the correct syntax here.

Try it like this:

use puppy;
DELIMITER $$
CREATE PROCEDURE spGetSystemLicensing
(
    IN  _licenseName varchar(128)
)
BEGIN

IF (TRIM(_licenseName) = '') THEN
    select * from SystemLicensing; 
ELSE
    select * from SystemLicensing where LicenseName=_licenseName;
END IF;

END $$
DELIMITER ;