Those are a kind of spring socket or spring header. They make proper, black plastic assemblies of these very much like the black 0.100" pin headers we all know (and probably either love or hate). Unfortunately, these are not generally available and are highly proprietary.
Digi, makers of the Xbee 802.15.4 mesh radio modules, is the only company to make these as far as I know. You can see them being used quite prominently on some of their developer boards:
Now, you can actually buy this part...Mouser even has them in stock.
Spring Socket from Digi
But they're $40. Probably because some poor bastard at Digi whose official position is 'proprietary connector fabricator and needle nose plier operations chief' manufactures them on demand. By hand.
Seriously, look at them. They are just right angle pin headers bent over. A solid flat surface and a pair of thumbs is all you need. Looking at any standard right angle header, they are long enough to reach all the way to be circuit board if you bend them down.
Now, the photo you're talking about is doing something a bit different, and slightly terrible. Those large
inductors spring connectors are clearly just antennas loops of wire, or possibly spring steel wire, soldered at both ends in the correct through hole pitched pads. They look like a short waiting to happen, and I would guess that they could not tolerate a curious kitty or table bump transient.
If you're looking for a good way to make a castellated hole edge socket, I have always just picked a pin header pitch for my holes and carefully placed them on my breakout board such that they are 6-10 mils too close to fit the module. You'll need to size the holes to the pin headers so there is virtually no give, and take into account drill tolerances and the actual width of the pin, but this technique is very forgiving.
See, when 'inserting' the module, you can angle it slightly and get one edge below the pins, and the tilt gives you enough wiggle room to push it against the other pins. Then you just push down to your desired level of snugness. If you have pins on 3 sides, as long as there is no lateral give, it will work without issue as well. 4 sides works with some effort, but its generally kind of a pain.