Does it favor a Heliocentric, or Geocentric Universe?
In a word neither. The purpose of the mechanism is clearly to position 'heavenly bodies' with respect to the 'celestial sphere', with reference to the observer's position on the surface of the earth. In order to achieve this, the mechanism has to use a geocentric model. However this does not imply that the manufacturer favoured a geocentric model of the universe. In fact it was Aristarchos of Samos (310 - c.230 BC) who first proposed a heliocentric solar system in 297 BC. Unfortunately proponents of the heliocentric universe were increasingly persecuted for their beliefs in Ancient Greece and in later times. It is highly probable that the maker of the mechanism was aware of the heliocentric universe, but it does not imply he favoured it.