The serial/parallel distinction is completely useless in here. But you're right on the pin count.
There are 9 pins in a full size USB3 connector, and 8 pins in a Lightning connector. But when the lightning connector has two data pairs, USB3 has a bidirectional pair for legacy, and two single-direction pairs for high-speed traffic. HDMI, and Displayport respectively have 3 pairs (+ 1 differential clock) and 4 pairs.
The real question is the nature of the signal on those pairs. USB2 is 480Mb/s with a lot of protocol overhead, HDMI has 3.40 Gb/s with only error correction, and USB3 is 5 Gb/s, but still has (parts of) its inefficient protocol. Depending from what Apple is doing, it could route only the high-speed signaling of USB3 on the Lightning connector's two pairs, and provide the same performance as a standard USB3 cable.
However, since Apple keeps all information about Lightning under wraps, only insiders can tell. And until now, all we've seen is quite underwhelming, with USB2 data cables, and now this adapter.