Well, technically Z gives the room a third dimension.
Setting it up requires that you give all the objects a Z value that interacts with each other. Floor, objects, etc.
Technically you can call Z integer whatever you like, like "altitude" or "height" or "pigglettsareblue", which ever is easiest to remember.
For floor, Z integer should naturally be 0 or it can be -5 or +5 for higher and lower elevations for an example.
For a Cat the Z integer should be indicated by distance between player's Z and floor's Z. If cat's Z is higher that floor's Z then it means cat is falling till it's Z indicator reaches below the floor value and then gets set to to value of the floor. As for items, if their Z index from the floor is like +10 then when it reaches half that number it labels object as "destructible" once it's value reaches the floor value.
That should be the gist of it on a theory side if any of that explanation made any sense.
Coding it in as intended is up to a user though.
Now of course you're going to need to adjust x value to match z value to create an illusion of isometric 3D so it doesn't turn out just to be a top down game
but figuring that one out shouldn't be a biggie.