This appears to be a circuit for commanding a "reset" by momentarily interrupting the power to the PIC MCU, triggered either by the depicted switch or if the optional jumper is installed, the RTS output of the USB-UART. It's not entirely clear why that method was chosen over driving an actual reset line, but the rest of the MCU circuit is not shown; perhaps in utilized configuration the MCU lacks a reset input.. - documentation indicates the MCLR pin of this PIC can be reconfigured as a GPIO without reset behavior. (That this is for commanded reset and not power saving purposes is indicated not only by the control signal sources and button labeling, but also by the fact that the transistor circuit defaults to "on" and will itself consume battery-draining power when "off")
The answer to your specific question on the usage of two transistors is because the desired operational "sense" appears to be that the MCU should be powered when the control signal is high, and de-powered when the control signal is low. A single transistor has inverting behavior, so a PNP element would give the opposite of the desired operation. Thus a second transistor is needed to invert the control signal: especially in the realm of digital on-off, most non-inverting circuits are actually a sequence of two inverting stages.
An NPN transistor operating as a low side switch would have the desired logic sense, but is inadvisable to use because it would mean breaking (and possibly introducing voltage differential in) a ground connection needed as a reference for various signals going into and out of the MCU. While N-type devices are more capable than their P-type peers and passive loads are often best controlled by a low side switch, logic devices would traditionally have their positive supply switched, so that the ground side remains integral. Worth also noting that for most devices, it is prohibited to have a voltage on an I/O pin outside the range of the supply; eg, when the supply is de-powered, though there are some exceptions. Hopefully the designers took that into account, or verified that the data sheet actually does permit whatever they did...