The game is 2D and tile based, but uses floats for entity movements that means you can be on two tiles at the same time.
If a player can only be on two tiles at the same time for the purpose of animation and otherwise he can only navigate horizontally or vertically, but not diagonally then your navigation points/nodes should always be the centers of the tiles and not the players themselves. When a player transitions horizontally/vertically between two tiles you should consider the player to be at the position of the tile nearest to him (if t < 0.5 then the source tile; else the target tile).
I took your image and plotted the waypoints/nodes onto it:
The purple dots are the navigation nodes and the lines connecting the dots denote where navigating from one node to another is possible (and only then and only along that line).