Well, the design resembles a class AB amp, but it is really "a class of its own". Not just a joke, let us explain the way this amplifier was developed over the years.
If you want to skip this part and go directly to the answer, click here.

Background, how and why our amplifier modules came to be:
We got a request from a subcontractor to Volvo many years ago. They had problems with a loop current amplifier which controlled the driverless trucks that moved cars from one assembly line to another. Sometimes they lost the track and could throw a car into the wall instead of onto the next assembly line. Not nice at all...
Well, we got involved in this project, and the problem was solved.
Some years later a subcontractor to "SL" (the bus-and-tube company in Stockholm) asked us to make an automatic two-way ticket booth amplifier. The problem was that it had to be placed in a metal box outdoors. So, the temperature could vary from -40 C (cold winter nights) to about +70 C (sunshine in the summer). The idling current should be as constant as possible over these 110 C variations, and it also had to be stable over time, as it should be used for at least a decade or more without need for any service or adjustments.
At first it seemed impossible, but then we remembered the current amplifier for Volvo. Using the constant current source, but making it work in another way, we solved the problem.Then a few years passed...

In 2005 we needed a really high sound quality amplifier to be able to test and demonstrate our first studio quality loudspeakers.
The amplifiers we had used before (NAD, Sony) were not good enough. We searched the market and found a few that seemed good enough, but they were far too expensive (several thousands of USD). So, we decided to build one ourselves. How difficult can it be?
Well, it took almost two years and about thirty prototypes until we were satisfied.
One problem was that we hade decided to use very fast HEXFET:s as output devices to get the best possible, detailed, sound. It was a class AB design, and it needed thermal feedback to stabilise idling current. But HEXFET:s temperature curves don´t match the bipolar transistos used for thermal feedback, so it took quite a long time to get this work properly.
Also, every single amplifier module had to be fine-tuned to the right idling current. And as the idling current was also dependent on power supply voltage, one had to have exactly the right transformer. If a lower voltage transformer was used, there was a risk of audible cross-over distortion.
Also, if one of the power supply voltages (+ or -) was lost, for example caused by a blown fuse, the amplifier produced a DC current, which could cause damage to the loudspeaker.
So, we only sold these units to people who were more-or-less experts.
After a year or two, we re-designed the amplifier so it did not have this problem anymore. Now the loss of - or + did not produce any signifigant output current. But still we had to set idling current and use the right power supply voltage.
However, after some more time we remembered the special amplifier we made for SL.
Could the same stabilizing principle be used also for a hi-fi amplifier using HEXFET:s?
We tested and it worked! No audible cross-over distortion, despite no thermal feedback and no adjustment.
Idle current was now almost independent of temperature, supply voltage or aging.
Finally it was ready for sale, also to non-technical customers.
There was only one drawback: When driving high BxL driveforce woofers without conjugate links at very low frequencies and high volume there were stability problems. Neither we or our customers had noticed this until one customer who had speakers with high BxL woofers told us he had found a track on Spotify where the bass sounded "fluttering". We played the same track, and at high volume we got the same result. (Our SQ-50 woofers have high BxL.)

We did some extensive studying about the phenomenon, and after a lot of work came up with the solution:
Separating the two current sources, switching from one-transistor current sources to a two-transistor configuration, and finally introducing a current mirror stage between the input and driver stages to further increase linearity and decrease sensitivity to reverse currents from loudspeakers.
So, from the initial design we had now gone from 7 transistors (inkl the HEXFET:s) to 16 per module.
But it was worth it! We now have an amplifier that produces no audible distortion of any kind. And (much thanks to the output design using HEXFET:s) with a brilliant clarity, with every single detail. And high BxL is no problem at all.

Now to the answer to the question: Is it class A, AB or B?
The short answer: No.
The closest would be AB, but with an important twist:

A normal class AB power amp needs thermal feedback from the power transistors (normally a small signal transistor mounted on the heat sink) to keep the idle current (relatively) stable. Initially it is set by adjusting a potentiometer. However, the small signal transistor and the power transistors don´t react quite the same way to temperature changes and aging. So after some years the idle current goes either down (causing cross-over distortion) or up (causing the temperature to raise, eventually destroying the amplifier) unless you re-adjust the idle current once in a while. Also, when playing music, the switching from one of the output transistors to the other is very sharp, which makes idling current level rather critical, so a re-adjustment once in a while is important for sound quality.