Shaft Encoder Accuracy
If the encoder only gives +1 pulse per 90 degrees, you aren't going to get better than 90 degree accuracy out of it.  

In the example code at the link, the val{x,y,z} are measured analog variables of some other thing that are sampled at each encoder lcoation: 


  My project is a data loger where three analogue inputs are sampled
  each time a rotary encoder pulse steps clockwise. On an Arduino, time
  is of the essence to get this data sampled and saved somewhere (I have
  not included the 'saving somewhere' part of this project yet.) In
  order to save some processor cycles, I have slightly redesigned the
  interrupt system to maintain a pair of boolean states outside of the
  interrupt loop.


These are not directly related to the positioning of the encoder, and there is no reason to think they provide angle information.