Replacing a switch matrix with diodes with a Analog Crosspoint 8x8 Switch
The datasheet shows that the switch matrix does not have the equivalent of the diodes in place: 


This makes sense as the matrix is meant to switch a variety of signals, and for most of the applications you don't want the diodes since they may interfere with the signal.

Whether this causes a problem for you depends on the use of the keyboard/keypad.

If you are creating a keypad where only one key is pressed at a time, then technically you do not need the diodes for isolation and the ADG2188BCPZ would work. But if you are creating an automated keyboard player where multiple keys can be pressed simultaneously, then you will need the isolation diodes and these can't be fitted to the ADG2188BCPZ switch matrix since you only have the X,Y bus pins available.  

There is a good explanation here for what is described as key ghosting, but if you're into PC keyboards it's usually called the N-Key rollover problem.

In your case with your matrix as shown:

 

Let's assume that PB0-7 are output bits from an MCU and that PR0-7 are input bits (you need to measure these with an oscilloscope to make sure). In this case a digital '1' on say PB7 would feed through one of the diodes on that column and a closed switch to provide the '1' signal at one of the PR0-7 inputs.
Since you can't provide the isolation required using the ADG2188BCPZ you'd have to do it another way.
I'd suggest the following:
  Since you obviously have an MCU (to drive the I2C interface) then you can use 8 bits of input to find which of the PB0-7 lines is high (or low if the logic works that way) and then simply set the PR0-7 line corresponding with that switch position while that signal is high. 
 You could use two NXP PCA9538 to do the task, one to sense the column lines and one to drive the register inputs. The PCA9538 is an 8 bit register that can be set for input or output and can even create an interrupt using a compare value for inputs. 

 

The scanning rate of keyboard such as you have is typically quite low, of the order of a few kHz maximum, so depending on your selected MCU you might decide you can build the code directly, or pass it off to something like an Arduino focused on the task.
You'd set up one PCA9538 to read the scan columns and one to output the keyswitch state for each column. You then don't need any diodes for isolation and only need 17 lines (PB0-7, PR0-7 and grnd) for your connection. You'd maintain your key state matrix in memory and transfer the values as each column comes around. You have to do this at the column scanning speed continuously of course.