Q3 is a phase splitter.
Q1 and Q2 are a push-push amplifier.
* connecting a center tapped transformer in the output circuit would produce a push-pull amplifier. This is how I was taught 50 years ago. Today the terminology may have changed?
Anyway the key is Q1 and Q2 bases are being driven out of phase. Q1 and Q2 operating class B (conducting 50% of the time) feed the load a full cycle with one transistor biased off while the other conducts. (or AB with one being throttled down while the other is driven harder.)
When Q1 is driven into conduction current flows from C1 DOWN thru Q1 to ground and UP from ground thru R3. Discharging C1.
It is a good earbud driver as I made mine but you can adjust the bias and add more power as desired.