I am unable to identify the exact piece of music used in the sample. This is simply because the given audio samples are way too short. I tried using apps that have over 10 million pieces in the database, but none had a single result.
I am able to provide some information though based on the samples with the knowledge I have about music.
At the very least I can say that the genre is either Jazz from the late 80s/early 90s or it is a sped up Soul track from the 60s. It contains drums and a very clear saxophone. The era is based on the playstyle of the saxophone. This playstyle was very popular during the 80s/90s. That is when the hiphop/jazz become popular in plenty of countries. While it is unclear if the actual audio sample used by the studio (Daume) has been tampered with is unclear. I looked up their history from around 2000-2005 and their connections to pinpoint a certain band that might've been used, but this provided no results.
As the second we can at least say that this soundtrack is from a legitimate piece of music and not made on the fly in the studio. This is because of the instruments used in the sample and the mixture of the instruments. This would be too expensive for such a short sample and would be too much hassle for a studio. There is a clear beat and the instruments dont conflict with each other; this indicates that the composer was aware of what he/she did; an experienced composer. If anything I'd honestly love to listen to this piece myself as well as it is a master piece based on what we were given to listen to during the episode.
Based on the genre and the airing of the series I'd say that it is from the early 90s. This is due to the big world wide hit on the genre Jazz at the time. But it might've been some Japanese Jazz as well, which would date to LP's from as early as the 70s.
Maybe with the information provided above someone might be able to pinpoint the track or LP. I don't think it will be found on the internet as not all music from the 90s and earlier are online. There are still some hobby stores around that sell LP's. Perhaps someone there can identify the piece. All you need to do is cut the first 10 seconds from the soundcloud track and then from 22s to 26s. Boost up the volume and you will hear the instruments clearly. But if the original file has been tampered with and for example boosted in speed then it is highly unlikely that even someone of that level will be able to identify it.