LC Oscillator Circuit Analysis
Q1 and Q2 are actually cross coupled because each transistor has its collector tied to the opposite transistor's base. This can be looked upon as a form of dynatron oscillator because R1 behaves like a constant current source. Where efficiency is more of a concern a choke is used for R1. If you tip the circuit upside down and redraw with PNP transistors then all will be clear to you.

There should be a cap across the inductor and the expected frequency is predictable. C1 is just a bypass cap and does not determine the osc frequency. Normally the output is taken from the junction of Q1 collector, Q2 base, and L1. Taking the output from where it's taken will give less output and lots of second harmonic distortion. This unorthodox output point may be useful if a frequency doubler is to follow.