It's hard to tell without component values but the placement of C2 is unusual. In combination with R3 this will form a time constant which will limit the rate of rise of the output when Q1's Base is being driven low by the input waveform. When the Base is driven high, it will form a lower resistance path for charging C2 again.
It would be wrong to describe it as Class-B amplifier though as there's always going to be some C-E current flowing through Q1, even if it varies a lot more than usual for a common emitter stage (again, depending on component values).