Starez is divided in a client and a server(for more information check the Architecture page), both with different dependencies.
Python
PyGTK 2.10
Optional: gnome-python-extras → If you have gnome-python-extras Starez will use the gtkmozembed module, to show game-information in an embedded web-browser. Otherwise Starez will generate a page with text boxes(little less fancy).
Autopackage → However, the client will install it if it's not yet installed(so you don't have to worry about this dependency).