What is this amplifier doing, exactly?

I read the datasheets for the maximum current of the transistors.
The current is 5V / (10 + 8 ohm) = 278mA, assuming no voltage drop of the transistor and the transistor being fully on.
At 278mA the BC337 has Hfe of about 250. So the 2k2 will turn it into saturation.

The NPN BC337 is an old transistor.
The NPN BC639 is a little newer, it can do 1A, and it has the BC640 as complementary PNP.

These are the prices in my country (a piece)
BC547B : 5 euro cents
BC546B : 6 euro cents
BC337 : 10 euro cents
BC639 : 20 euro cents