That about sums up the main parts of the code. Your challenge, should you choose to accept, is to improve upon what we have done here. The next logical step would be to use the built in data logger feature of the Ultimate GPS module, and map your dog walks when you get home.
This project was completed in 2012. Advancements in parts are such that this project might be more easily done on a board such as a Feather M0 in CircuitPython.
As far as replicating the original project: Adafruit now carries the original ATmega32u4 processor on the Feather 32u4 Basic and Feather 32u4 Adalogger boards. The latter provides an SD card capability good for data logging. At present we do not have diagrams and code to implement the project with these boards but the changes from the original processor board would be very small. The boards are listed in the Featured Products page.