"And yes, it is a grounded base Colpitts oscillator. You have to see the 680p and the 33n in series which makes 666p to which the 200p have to be added - a total capacitance in the parallel tank circuit of 866p. Together with 1mH you obtain a resonant frequency of 171kHz. There is no magic..."
"There is so much metal around the antenna that you can't consider the static antenna capacitance being only 7pf but rather the double. This would explain why the author of this article was happy with only 40mH (and we are even not sure about that!)."
My spreadsheet sim shows about 20pF at the antenna for a 172kHz resonance point. Even with all that metal this seems kind of high to me, but I haven't delved into the antenna math (yet). That, and I guess I'm too busy talking to know anything. ;)