Yes, of course. But they have the the actual transfer of the raw data offloaded onto specific circuitry that mostly just passes it through, something the processor part of a SOC would be terrible at. That's not what Apple is doing; they take in a normal lossy compressed video stream (H.264, who knows) and then reconstruct a HDMI signal.
The only difference between what you've described and what is going on in this adaptor is the inclusion of h264 decoding. The use of this is an argument that can be had (personally I think it was a great play on Apple's part, see my comment here: http://news.ycombinator.com/item?id=5308345)
The rest of this is ancillary stuff. They aren't decoding h.264 on an ARM core, that's impossible for any significant bit rate, they are doing it with a purpose built bit of hardware, just as the HDMI encoding is done in a purpose built bit of hardware. Incidentally the encoding of HDMI is a mess, the spec is worth a read some time.
