XBee and ZigBee for long distance signal transmission
All the clues are in the answer linked to in your question. Here's a recap: -


Using minimum data rate (20kbps) you need a theoretical power at the receiver of -111dBm
Free space link loss at 10km is 120dB (use the formula - I've used 10km and 2.45GHz)
If output power from transmitter is +10 dBm, receiver power is -110dBm


That's almost a perfect match and remember this is almost equivalent to a free space set-up because the plane is high. Also, the ground antenna used has a gain of 14dB, so now the set-up is 15 dB better than free-space theoretical.

Also, I believe zigbees can be used at lower frequencies than 2.45GHz, something around 1GHz and if so, this adds another 8dB improvement so now we have a theoretical margin of about 23 dB. There isn't enough info in the article about the plane to determine this.

On the ground, this is not reliably possible (as explained in my linked answer), but as a one-off experiment where the transmitter (plane) never went out of site of the receiver this  was clearly possible.

EDIT

If you look at the specification of Xbee Pro (the one used by the guy flying the plane), it's operating frequency was 900MHz and if you check on page 7 it can transmit at +24dBm and use a bit rate of 10kbps.

All these little things, when thrown into the pot can make a difference between a usable system and a system that will never work. It's a fight (for sure) and you need to use every scrap of advantage you can grab when making a reliable radio link.