How can this capacitator discharge? (Make: Electronics experiment 9)
Yes, you are correct. The meter will give a deflection when A is pressed but none when B is pressed.

The circuit does not look very good. 


The 10k resistor is in-circuit when A is pressed and will limit the current in the circuit to a peak of \$ I = \frac {V}{R} = \frac {9}{10k} = 0.9 \ \text {mA} \$.
B, however, just shorts out the capacitor as you noticed. This is generally not done as there is no current limiting other than the internal resistance of the capacitor. The high initial current may cause arcing and damage the switch.


I would think that they wired it that way to prevent a dead short on the 9 V supply if A and B are pressed simultaneously.