The version on the CD isn't terribly long, so I'm guessing that was the opening cue for the show. From what I can remember from watching show closings during the original airings, the end theme was the exact same - only longer. It basically just repeated the same verses over and over - in other words, we're not really missing any passages on the CD.
Interestingly, on the 1987 "This is Your Life" special with Betty White that's floating around, they play the '70s "Password" theme during one of the introductions. It's done by an orchestra or something, but I find it interesting that out of all the "Password" themes, that was the one they chose for that introduction.