That musical section of Herb Alpert playing the theme was not included on the soundtrack album. The album has a different "score" instrumental that segues with Lani's standard theme tune. The YouTube uploader took the music from a LaserDisc.
One thing that's always driven me crazy with that movie's soundtrack: no matter which version I've ever watched, there's always a noticeable "wow" in the music, particularly noticeable in Lani's song, it's like an off-center record.
CD soundtrack from Silva Screen is now quite pricey being OOP.
I saw the movie in the theater in 1983 and the last scene in the movie and closing credits had Herb's trumpet solo and I loved hearing it and I still do its too bad that version. Never got released it segues beautifully with Lani's Main theme. To me that qualifies as a Rarity