Hi:
The short answer is - you can't.

You can't mount the Puppy file system because it doesn't exist in the same manner as it would if Puppy were installed on a real drive partition. It's being emulated by QEMU. The Linux 'drives' you're trying to mount don't 'exist' as Linux partitions unless QEMU-Puppy is running. The rest of the time they're just part of the data file used by QEMU.
The QEMU-Puppy website has a better writeup than I'm giving you. You might have missed it, so I'm quoting it below:
2.2. QEMU
From the site: "QEMU emulates a full system (for example a PC), including a processor and various peripherals. It can be used to launch different Operating Systems without rebooting the PC or to debug system code."
In other words: QEMU is a virtual machine. A virtual machine is a program that acts like computer hardware. In such a virtual machine, you can install an OS (Linux, Windows, BSD, whatever). This OS "sees" a processor, which is the real processor (I'm lying...), "sees" a hard drive, which is a big file on the host machine, "sees" a network card, which is emulated by QEMU, and so on. After shutting down the virtual machine, all that's left on the host (or USB memory stick) is just one big file: the virtual hard disk.
From the point of view of the host OS, QEMU is just a simple program which allocates a lot of memory, eats a lot of CPU cycles and opens and closes a couple of files. That's it.
When you think about it, you've answered your own question:
the file system I want to mount is not a partition - it's just a file!
Yup. That's exactly right.
