How is this small drone able to transmit video to such long distances? And that too an HD video?
I don't see why not. First find a suitable low power encoder IC: https://www.fujitsu.com/downloads/EDG/binary/pdf/find/27-2e/2.pdf will do Full HD at 500mW, so assume 1/4 that for 720p/30. Squash the bitrate down to 1.5Mbps then there are all sorts of radio systems which will do that easily at low power. The distance is higher than normal but may be achieved with a directional antenna or (because this is military) use of other bands and the 2.4GHz everyone else is squashed into.

1.6km (or "a mile") is easily achievable by a mobile phone to its base station.


  I am still unsure why a pair would cost $40,000.


That's a separate issue. Probably because they're made to military standards, including reliability and traceability, and in small quantities.

There are lots of toy drone + video systems that are much cheaper.