13Bit Encoder interface for microcontroller
All of your parts will "work", in the sense that they will allow simple communication between the encoder and your Arduino. They will not, however, do what you want.

The labels on the encoder lines establish that they are quadrature encoded with a home line which will become active once per revolution. This is not serial communication in the same sense as, for instance, RS232. Instead, a transition on either the A or B lines indicate that the encoder has moved by 1/(2^13) revolution.

It is entirely possible to use such a protocol directly. What you do is feed both the receiver A and B lines into IO lines of the Arduino. Monitor both lines and if either changes determine the direction from the state of the other line and update the shaft position.

Of course, you may or may not be able to keep up with the computation requirements. If the shaft is turning at 60 RPM, or 1 rps, then you'll get a change every 125 usec. Furthermore, if you're doing anything else with your Arduino, and you're monitoring the encoders by polling, you'll risk missing a transition while performing those other tasks. You can get around this by setting the two lines as interrupts. See, for instance, here or here

There are dedicated quadrature encoder chips, but I'll leave such fundamental search tasks to you.