It is important — actually, critical — to read the Terms and Conditions when making purchases on the Internet. When purchasing a service (trip) from Southwest Airlines Vacation, you are not making a purchase from Southwest Airlines Co., but from The Mark Travel Corporation.
Yes, "Southwest Airlines Vacations" does use the "Southwest" name and likeness of a SWA plane (presumably under license from SWA), but purchasing a service/product from "Southwest Airlines Vacations" is not the same as purchasing a service (an airline ticket) from Southwest Airlines Co.
In addition to the quotes above stating the paper ticket is required for travel, the Southwest Airlines Vacations website clearly states "The Mark Travel Corporation is the tour operator for Southwest Airlines Vacations" and the copyright notice at the bottom of the page (which few pay attention to) reads "Southwest Airlines Vacations, a division of The Mark Travel Corporation."
I would not have high expectations of recovering the value of the unused/forgotten paper ticket.