Most hardware video decoders are special-purpose DSPs that the manufacturers write firmware/microcode for to decode particular formats. The instruction sets of the DSPs are well suited to operations normally performed when decoding (or encoding) video.
> If I'm not mistaken they're not general purpose computers. If they were what would be the point? Why not use a math coprocessor?
They are not general-purpose, but that doesn't mean they're not easily re-programmable either. Consider the example of GPUs.
I want to say some SNES games used a DSP chip, there are several known to emulator authors, including two versions that used the exact same hardware with different microcode (and therefore different abilities). So it's been done before at least.
DSP's are like processor units in GPU. Optimized for fast and parallel multiply and add computations (and some other basic signal processing stuff). One codec is not that much different from other from computation point of view.
The accelerator units are usually filters that operate over a region of memory while processor is busy computing something else. These can be made fixed function, however most of them are programmable to support multiple steps in codec processing.
2) If I'm not mistaken they're not general purpose computers. If they were what would be the point? Why not use a math coprocessor?