Loudspeakers have very low resistance (called impedance as their resistance changes with frequency). The output of the first stage has more resistance than the speaker. Therefore the speaker will need more current than the first stage can offer.
The circuit in Fig 5 is an example of the second stage circuit. It is called a Push/Pull Amplifier. It uses two BJT transistors connected in Common Collector configuration. In this mode they do not create any voltage gain, they can only pass on the voltage level from the first stage. But they do have very low output impedance. Meaning that they can supply a lot more current to keep up with the speaker’s demand. Hence, a current amplifier.
When there is an input signal at the first stage (‘Vin’ Fig.4), the resulting large voltage swings across Rc and Q1/RE (in Fig.5 shown as R, D1,D2 and lower R) impress against T1 and T2. This voltage swing carries through to the speaker and the two Common Collector transistors take care of the current needs. The push pull circuit uses two opposite polarity transistors (NPN and PNP), so one can supply current for the positive half of the voltage shift and the other for the negative half of the shift.