Replacing existing and working 3way with smart switch
I think your wiring situation looks like this 



I believe it is a 3-way circuit, and the lack of any red wires, indicates the person used a cheat: using two 14/2 cables paired when he should have used 14/3 (with the red wire).  So this accounts for two cables in both boxes.  This leaves only one cable in the "smart switch" box.  With only one cable remaining, that can only go to the lamp, meaning power is coming into the lamp, not the switch.  The entire 3-way complex is a switch loop.  

Since all your wires are black and white, I took the liberty of adding tape to color-code the actual functions. Where a wire is taped, think like the tape color is now the wire color.   Now in any of these cables, it may be used the other way around, e.g. white for switched hot.  In the 2-cable segment, any wire  can be any of the functions.   I am guessing. 

I use yellow for both messengers because they both do the same thing, are both interchangeable (you can swap them and it won't do any harm).  However they are not the same, landing both messengers on one screw terminal will not work.  

Note that in the first (right) switch box, there is always-hot and switched-hot.
There is no neutral in a switch loop.  Ergo you will not have much luck making that smart-switch work.