It is a side effect of the so-called "cookie". When the bootloader starts, the first thing it does is to check a special "cookie" in memory. If it is cleared, it continues the bootloader. If it is set to a special value, however, the bootloader starts the original firmware.
The idea is that the bootloader sets the cookie to the special value when it runs, and clears it when it starts Rockbox. Therefore, if the bootloader crashes, the cookie is still set, and if you reboot it will start the original firmware, so you are able to reflash the broken loader.
Now, the double-click behaviour you see is an effect of this, and actually a bug in the bootloader. The bootloader checks if the ON button is held, and powers off if it isn't. This is to prevent Rockbox from starting if the ON button is accidentally pressed in your pocket or bag.
However, the bootloader forgets to reset the cookie in this case, and if the ON button is pressed again very quickly, the player starts again and the memory has retained the cookie value even though it has been powered off, and Rockbox starts the original firmware.