Good find! The person who posted the clip is slightly off on the years the music was used. Believe it or not, elements of it actually were still in use until 2000. The last surviving pieces of it were cuts used for reports during the annual Houston Livestock Show & Rodeo as well as the spot that ran each night before the rebroadcast of the 10 PM newscast during the late night hours (with the 1994-era graphics). The first phase-out came in 1996 when they re-branded their morning show to "The Spirit of Texas This Morning" and used a separate package for it - one that the NMSA has lumped in with The Spirit, though I'm not sure if that's actually the case.
With regard to the music... listen to the intro of Giff Nielsen's Bulls Eye... Is it just me, or does it sound like a Stephen Arnold piece? It is not part of the American Spirit package at all - I have the 3 discs of it. Wonder if anyone has any insight into that.
It also made me realize just how a dedicated weekend sports show (outside of High School sports) has never really worked on the station. I can think of a bunch from 1990-2005 or so that were there and gone in short order - The Sports Page, Warren Moon's Quarterback Corner, The Jack Pardee Show, this one, a show with Giff Nielsen and Dan Pastorini in the early 2000s... The current Sports Extra has had some staying power as it started in the 2010s, though.
Fun, somewhat irrelevant fact - Kathie Turner (the weather forecaster in the clip) actually helped me get my meteorology merit badge when I was in the boy scouts. This was also a great excuse to go to poke around the station during the late 90s and see that great MBD set when it was still fairly new!