What type of voltage booster circuit is this?
It's a non-isolating self-oscillating flyback converter.

Pin 5 from the transformer provides positive feedback to make TR106 oscillate.

When the transistor stops conducting Pin 3 goes positive, D101 conducts and charges the output capacitor, C116.  L104 and the following capacitors filter the output.

When the output voltage reaches the set point (12v), zener diode ZD101 starts conducting causing TR107 to divert base current from TR106 and either stop or reduce the level of oscillation.

It is surprising that a transformer would be used for such a small step-up.

A non-isolating booster would normally use just an inductor in the collector of the main switch transistor (TR106).  It is not so easy to make it self-oscillating though and would require a different arrangement.

Alternatively with the same circuit D101 could be fed from the collector of TR106 and reduce the number of windings on the transformer.

One advantage of a separate winding for the output is that in the case of a short circuit on the output the circuit stops oscillating and the fault current is low.  With the conventional step-up the short circuit current can flow directly from the incoming power supply (9V in this case) through the diode to the short.