The player location is stored using an array. Three variables are used as coordinates X,Y,Z.
The X,Y are the map coordinates, while the Z is the height.
In order for the game look 2.5d when its 2d the entire the lower floor (Z-1) map is moved and has the X and Y coordinates transformed (Y-1) && (X+1). Which creates a nice illusion of 3d background. It also makes changes to the general way the 2.5d coordinate system, I do not remember how did they.
The entire process of the illusion used in 2.5d games is explained in this post, it works really similar to the U7: Perspective projection with 90 degrees between X-Y axis?.
When a player uses stairs he is simply transported, his coordinates are changed and he is transported/teleported to the ground tile the stairs lead to the right. Generally it would work the following way [x+1][y+0][z+1]
It actually isn't pathfinding. It just moves you around the tiles just like teleporting would do. There is no need for a method to avoid obstactles unless you are making a movement method to the stairs~ itself:)