reading the encoder pulses without the Encoder library

I don't see anything in the datasheet which would cause you to say

I have an analog require encoder I mean that the channels of the encoder must be connected to the analog pins of the Arduino board,

In fact Note 1 says

1.The output signal is open collector structure

This would indicate a digital input with a pull-up resistor to Vcc.

Please explain why you think this encoder must be connected to the analog pins of the Arduino.