That's right but Brad for example still produces/engineers most of the LP songs, an album is band product. They all have they their input on it someway, even if it's just an opinion or just a blessing that they like it, that's probably the difference.
If they only credit those 4 it's for a reason, maybe they were not interested or didn't care to work on music for the movie, or wanted to take time off, or work on THP, who knows.
Maybe they didn't want the soundtrack to be a band product, more as a side project that it doesn't interfere with the "real" LP music.
The track is great, the 2nd part is a bit weird since we haven't heard it yet. Just take it for what it is, why do we always have to compare it to X and Y when something new comes out? It also happens when a LPU CD drops when there are some real songs on it.
I can really understand that with Living Things but Hunting Party is more than a solid record. it's raw and heavy, that's not something that we all expected at this point especially after Living Things.