Why are the capacitors in this circuit in parallel but not in series?

They are in series, one end of the first capacitor contacts one end of the other. They are also parallel when the switch is on, because they both connect two ends.

Parallel connection means both ends of the two elements are connected together. This happens when you turn the switch on. Both ends of C1 becomes connected to both ends of C2. Before that, only one end of C1 is connected to one end of C2. The two remaining ends are open.

I assume that this is an example where one charged capacitor charges another after the switch ic closed.

The main use of assigning the labels series or parallel to capacitors (and other circuit elements) is to decide which combination rule to use to find the effective capacitance of a number of capacitors.

The derivation of such combination rules have assumptions in them: the magnitude of the charge on a capacitor plate is the same as the charge on the plate of another capacitor to which it is connected in series and the potential difference across capacitors connected in parallel is the same.

So considering the final state of your circuit after the switch is closed which of the series or parallel conditions is going to be satisfied?

This is a nice question, Consider this circuit first, that build from one resistor and battery,

We can apply kirchhoff's law and we can get that $$V_R=V$$ while $V$ is the battery voltage, thus we can say that the resistor is connected parallel to the battery.

Now check the following circuit,

We can see that applying kirchoff's law here will yield $$V= V_{R_1} + V_{R_2} +V_{R_3}$$ so now the resistors is connected in serieis.

According to your question, this case is similar to the first circuit I mentioned, because the capacitor $C_1$ is charged, it can used as a battery source for the circuit and $C_2$ will be in the role of the resistor (it's just for analogous for the first circuit, of course there is difference between capacitor and resistor) , thus we can get from kirchoff's law that $$V_{C_1}= V_{C_2}$$ wich means that the capacitors are connected in parallel.