I've noticed a trend in almost every game put out by Squaresoft/Square Enix on the PlayStation 2. All the files are hidden except for the IRX files, the ELF executable, and SYSTEM.CNF. The attached screenshot is from the US release Final Fantasy X, but this also applies to a few other Squaresoft/Square Enix PS2 games I can think of, such as Kingdom Hearts I, II and Re:Chain of Memories, Final Fantasy X-2, Dirge of Cerberus: Final Fantasy VII, and Final Fantasy XII.

Here's my question. How can I go about ripping the hidden files - textures, images, FMVs, audio, text files, and models - from the aforementioned games? Do any tools exist that can deal with such PS2 games that don't use the standard ISO9660 filesystem?

I remember this topic was already discussed on non-existent xentax forum, so you can search through backups to find valuable info on this.
I believe there were some scripts that could help you with reading and dumping data from ISO sectors directly.

I believe you've pointed me in the right direction. I'll definitely be looking for those scripts and I'll report back when I find them.