Lightning doesn't do USB 3.0, so you can safely assume that the bandwidth of the port is less then 5gbit/sec.
HDMI runs at 10.2gbit/sec. At the bare minimum, Lightning is at least half as slow as required to properly support a full HDMI link. There simply aren't enough pins and data doesn't move fast enough to make this happen.
The old 30-pin dock connector was capable of a full 1080P link because HDMI was handled on the device and passed through the 30-pin connector relatively unscathed, so it was literally just a wired adapter with some other bits and bobs strapped in to stabilize the signal...
I think you're confusing the capability of the port and the capability of the SoC. There's no reason why you can't push a 6 Gbit/s full-duplex signal through the Lightning interface. The iPad mini and iPod Touch (5th gen) are both powered by the A5R2 SoC though, which is based on an older design and has no Lightning specific capabilities.
Regardless of the physical connection, mobile devices tend to provide digital display output by methods that serialize as much as possible to reduce pin count. You've got FPD-Link II/III, MHL, MyDP, etc, all of which can operate at relatively high bit-rates (certainly well in excess of USB 2.0). Conventional HDMI actually uses 3 TMDS channels at 1.65 Gbit/s for 1080p.
It has never been clear to me what format the Apple 30-pin dock connector used for digital video. Existing pin assignments make it unlikely that anything approximating a conventional HDMI signal was used. Both Lightning and the 30-pin dock connector support 1080p30 output, HDCP, and conversion to HDMI via a device powered adapter. Some general assumptions can be made that the number of signaling pairs used for digital video is not more than 2, and that the bandwidth provided is at least the 1.24 Gbit/s required for 1920x1080, 18 bpp, 30 Hz using CVT-R. MHL and MyDP are both off the table for various reasons, so that leaves MIPI DSI, FPD-Link or something I'm not thinking of.
I wish it was. Unfortunately, it isn't. It seems it's just an AirPlay receiver (without forcing the user to explicitly set the client to stream), with all its associated problems: (when not streaming iOS-native video files but, say, mirroring or playing back non-iOS-native videos) low framerate, lowish resolution and a lag making it impossible to play fast-paced (action / racing etc.) games.
(Note that, not having purchased the new adapter myself, I don't know about whether iOS-native video files are handled the same way as on the AppleTV. As the latter has 8GB caching storage, it can pre-buffer streamed video just fine. Here, the lack of buffer MAY mean this adapter can't even play back iOS-native video files properly, unlike the ATV.)
That is, unlike the old HDMI / VGA adapters (which did mirroring without problems), there's no point in preferring this adaptor over the old, true AirPlay-to-AppleTV way. That is, don't purchase this if you already have an Apple TV - this won't offer any (resolution / framerate / lag) advantage over streaming to the AppleTV, unlike with the previous adapters.
All in all: I'm VERY disappointed. I loved the old adapters, which I used a lot when I needed much better performance / quality than with AirPlay (again, except playing back iOS-native videos, which are played back flawlessly if your network is fast enough not to have buffering problems). However, given that this adapter doesn't seem to offer anything over AirPlay (on the contrary: it may not even decode iOS-native files natively), I surely won't purchase it.
Apple should have gone the separate micro-HDMI way, as has Nokia, instead of - even when compared to Apple's previous tech - just offering us a technically vastly inferior "solution".
Well, but it isn't like AirPlay at all, because there's no WiFi involved whatsoever in this situation. There's no radios in Apple's adapter, and that has serious advantages.
I still have many questions about this whole situation. Were the Panic crew using video out or video mirroring mode? Because while the iPad mini supports playback at 1080p30, the screen is only 1024x768, so to mirror that 1:1 to a 16:9 display with letterboxing would yield... 1366x768. Yeah, I got nothing.
I also wonder what's in the other end of the adapter. Panic only showed us one end, and we all know how Apple likes to cram silicon into tiny spaces. The cable was also cut down to a nub, so although it looks from the solder pads that the cable uses 9 conductors (1 for each pin of the Lightning connector), it's hard to say for sure. I did spot 1 NXP chip on the board, but at a glance, it didn't seem to have the full complement of chips we've come to expect from Lightning cables/accessories. I also couldn't make out if one or both of the differential signaling pairs was being used. Another possible reason for using an ARM SoC in this device is because it has a Lightning port of its own, albeit solely for power.
One last theory to throw out there is that because the iPad mini and iPod touch (5th gen) are both still using the older A5, they don't support a digital video signaling mode appropriate for Lightning and are therefore sending the H.264 AirPlay versions of the video data via USB 2.0 to the adapter.