A lot of modern hardware coprocessors are hybrid blocks that can be configured through firmware. You can dedicate a very small DSP with the block to feed and manage it. I haven't been involved in a new chip design in a few years, but a lot of specialized cores were vector processors (very narrowly defined vector processors). I don't know if that has changed.
I find it surprising that you have a graphics card that won't decode new video formats, unless the vendor has completely abandoned support for it. I have never encountered a modern graphics card that wasn't completely configured and run with firmware.
Maybe I just don't pay attention, but I've never heard of new firmware going out to multi-year old graphics cards and adding new features. Sure it may be possible, but what company is going to go through the trouble of that?
I find it surprising that you have a graphics card that won't decode new video formats, unless the vendor has completely abandoned support for it. I have never encountered a modern graphics card that wasn't completely configured and run with firmware.