I'm not the expert but certainly contact the people department to get the straight ruling but I'll take your post & try to get an "official answer" from the folks who do know. Here is the "clarification" that might make it easier to understand.
As the website says, flying from the left seat as sole manimupaltor of the controls is generally interpreted as the person who signs for the aircraft also. Since most CAs fly in the left seat the logic applies & even when both folks are typed, the most common practice among most pilots is that whoever flies in the left seat is also signing for the aircraft.
When doesn't this happen? When someone is getting upgraded to the left seat & the IP is sitting in the right seat...the IP is signing for the aircraft. What SWA is attempting to do I believe is to eliminate the crews who under their work rules logged PIC time since both folks were type qualified...this can't happen from SWA's standpoint...either you signed for the aircraft or you didn't...if you did, you can log the PIC time, if you didn't, then it was PIC time or other time (observation, flying in the back, etc.)
What I would do is if you have not broken your time out into this type of trackign system then do the best you can to give yourself a reasonable proportion of PIC time when you were flying under your company rules...take 50% for example if you believe you can answer the question truthfully & your log books can pass the test. Again, be conservative & don't try to fudge the numbers...it isn't worth the risk & more importantly it isn't what SWA is looking for.
Pretty simple, sit in the left seat & signed for aircraft=PIC time
Sit in right seat, signed for aircraft=PIC time
Sit in left or right seat, didn't sign for aircraft=SIC time
Hope that helps,