In the case of Apple AVD, it's a multi-stage system with a bunch of special primitives, orchestrated by a Cortex-M3 with firmware. Codec-specific frontends emit IR which a less specialized backend can execute.

https://github.com/eiln/avd

This really heavily depends on the device, though. There are all sorts of "hardware" video decoders ranging from fairly generic vector coprocessors running firmware to "pure" HDL/VLSI level implementations. Usually on more modern or advanced hardware you'll see more and more become more general purpose, since a lot of the later stages can be shared across codecs, saving area vs. a pure hardware implementation.