Timing play or not?

[Illini_Ref]

I just need to know WHICH out does the swing appeal count as, the second (which is when the K happened) or the third (when it was called). If it is considered the second out, then we have a timing play. If it is the third then we don't have a timing play and no runs can score regardless.

It just seems that this appeal is different from a "normal" appeal of say a missed base. In a check-swing appeal the non-primary umpire is changing the call of the covering umpire, in essence. In a normal appeal the calling umpire is simply holding his call until asked for it.