Well, actually, not "quite" a Class A design. Class A is intended to bias the transistor
into its linear region of operation, but you'll never get that with the ckt as shown.
It looks like the person who designed it had the intent of Class A, but you would need
a resistor in the emitter lead, so the 100Ks on the base have something to bias in
a stable fashion. As it is, they simply turn on the transistor, and whether or not the
collector sits at Vcc/2 is strictly a factor of the hFE [beta] dc current-gain of the
transistor.
But there is a much more serious problem with this design, namely that there will be
a constant dc-bias on the speaker and a non-trivial amount of dc-current continually
running through it. Not good, the speaker can burn up. Instead, speakers should be
AC-coupled through a large capacitor with a ckt like this - ie, attempted Class A. And
unfortunately, that cap needs to be a large value, eg 220 uF, to get proper low-
frequency response, since the speaker impedance is so small.
Also, with a proper Class B, as Krupski mentioned, the positive and negative drive
ckts will be adjusted so the DC current through the speaker is 0, so that takes care of
the problem of continuous current burning up the speaker.
Advice - throw this ckt away, use something better.