Thanks for the script, aluigi! I made some progress (sort of). After looking into the files a bit more, it appears as if only some of the .BOX files may actually contain texture files, although that doesn't make a whole lot of sense to me.
I found a program called "PSXPrev", a Playstation texture and model format scanner. After a scan, another menu is supposed to pop up to allow browsing of the results, but that feature doesn't seem to work, unfortunately. Anway, some of the scan results:
"Scanning for TIM Images at file E:\Deathtrap Dungeon\BOX\BOX\BELFRY_B.BOX
Found TIM Image at offset 20A754
Found TIM Image at offset 26F9E8
Scanning for TIM Images at file E:\Deathtrap Dungeon\BOX\BOX\CIRCUS3.BOX
Found TIM Image at offset 298638
Scanning for TIM Images at file E:\Deathtrap Dungeon\BOX\BOX\DRAGON01.BOX
Found TIM Image at offset 242F04
Found TIM Image at offset 242F58
Found TIM Image at offset 244EA0
Found TIM Image at offset 244EF4
Scanning for TIM Images at file E:\Deathtrap Dungeon\BOX\BOX\DRAGON03.BOX
Found TIM Image at offset 24088C
Found TIM Image at offset 240A8C
Found TIM Image at offset 240B84
Found TIM Image at offset 25C7C0
Found TIM Image at offset 265618
Found TIM Image at offset 26564C
Scanning for TIM Images at file E:\Deathtrap Dungeon\BOX\BOX\PITF.BOX
Found TIM Image at offset 25AF28
Scan End 10/16/2018 16:03:34
Found 14 Textures"
So now we know the texture format for this game is .TIM, a common PS1 format. It's not much, but i'll stick with it and see what else I can find. I've attached a couple Dragon files if you're interested. For PSXPrev, it can be downloaded here:
https://github.com/rickomax/psxprev/releases and usage info can be found here:
https://ricardoreis.net/?p=23