What do you mean with "processor" exactly? The Dingoo uses the JZ4740, which is a system on chip (SoC). This means both the CPU (the actual processor) and a lot of peripherals (LCD controller, sound processor, SD controller, memory controller etc) integrated into a single chip.
If another system uses the JZ4740, Dingux could be ported to it. But it does require some customization, since for example the GPIO (general purpose input/output) pins will be connected differently. On the A320 these GPIO pins are used for things like the buttons, the LCD backlight and powering on/off various external peripherals. The Dingoo A320 and the Ben NanoNote now use a single source repository (qi-kernel) for both devices, but the kernel configuration is different and there are two device-specific source files. Still, the vast majority of source code is shared.
Like zear said, for user space (applications) it is easier to be compatible. Especially if applications use standard interfaces as much as possible, which is one of the goals we have with OpenDingux.