What is a "phase reversal" choke and why is it used?
This is subtle. 

Remember that T2 is a TRANSFORMER and obeys the usual transformer rules (to a first approximation). 

Lets assume Q1 is turned hard on, so the winding 3-4 has the full supply voltage across it, magnetising current flows and voltage is clearly induced in the 1-2 winding which due to the way the thing is phased, adds to the supply voltage as seen at Q2s drain, but Q2 is turned off... It is this voltage that pushes current thru the load T1. So with Q1 hard on, The current flows half to Q1 drain thru T2 3-4 and half to Q1 drain via T2 1-2 and T1 primary (But T2 boosts the voltage available to this path). 

Of course this current flowing in T2 1-2 causes current to flow in T2s 3-4 winding, so energy is conserved. 

On the other half cycle the behaviour reverses and power is transferred the other way thru T2. 

The overall effect is that the current in the T1 primary is half the supply current, but at about twice the voltage.

There is actually another subtle trick you can do with T2 (But that the packer does not exploit) in that if you squint just right T2 is a 4 port hybrid which has the second harmonic power appear on the 'DC input node', this can be exploited to lower the second harmonic content albeit usually not by quite enough to remove the need for further filtering.