The news is light on the tech side of things, but I wonder if their experience building their Aereo antenna infrastructure might have a place in this.

From the video, it appears that their goal is to have a few transmission towers in a region and then neighborhood or block-level repeaters that receive the signal and rebroadcast it.

So, fixed millimeter microwave wireless from the repeaters to the main gateway, but what will they use from the repeater to the customer?

Some WISP's are starting to roll out 4G hotspots over unlicensed frequencies. That would work in this situation and their experience with micro-antennas could let them cram several antennas into their router to connect to as many of the relays as possible to increase bandwidth and resilience.