The Arduino Nano uses an ATmega328 processor instead of the ATmega32u4 used on the Arduboy.
The ATmega328 only has 2K of RAM instead of 2.5K. It also has a different USB interface. These and other differences mean that not all Arduboy sketches would be able to run on a Nano based system.
However, a while back I ported the Arduboy library to work with the Nano and other ATmega328 based boards. It's incomplete and out of date so it may need some work to get some sketches working on it, especially if they use the newer Arduboy2 library and other Arduboy support libraries.