You still have Wild Shape.
When the archetype says it replaces the old ability for a new one, scrap everything on the old ability, but use the new one similarly to how the old ability worked, with the new exceptions.
The text for Naga Shape is:
Naga Shape (Su)
At 6th level, the naga aspirant can use her wild shape ability (gained at 4th level, as normal) to assume the form of a true naga. This effect functions in a similar manner to a shapechange spell with the following exception. The druid's true naga form is unique, representing her personal evolution. When taking naga form, the nagaji's body transforms into that of a large serpent, though she keeps her own head. (...)
This ability otherwise works like and replaces wild shape.
Which means you do not have the default Wild Shape anymore, you got the archetype's own version of Wild Shape (obtained at 4th), plus Naga Shape (obtained at 6th), which works exactly like Wild Shape, using the same durations and uses per day, unaltered as if it was simply an extra option for your Wild Shape ability.
So at 10th level you could change into Animals (Beast Shape 3), Plants (Plant Shape 2), Elementals (Elemental Form 3) and Naga Shape, for 10 hours, 4 times per day.
The fact that the Naga Shape's text says that it replaces Wild Shape means that you cannot take another archetype that also replaces Wild Shape (see archetype stacking).
Another point that should be considered is that the Treesinger Elf Druid Archetype (from the same book) does state that you cannot assume an animal or elemental form. The text of the ability is otherwise very similar to Naga Shape's.
But i agree that the text on this archetype is confusing and could suffer table variation. There is also a FAQ request at paizo.com about this archetype.