I haven't actually decided the best way to actually find the pathway, I just wanted to throw that stuff out there because it does seem useful but it is so far incomplete work (I'm still working on it).
Also, what I posted is just conceptual and all that stuff is precomputed, and it only requires a lookup to get a value which just tells you
a) if there's a path
and (more importantly)
b) how many ways you can get from tile X to tile Y and
c) in how many steps it takes (represented by the matrix power)
Well, I see what you are saying. I mean, of course you need vector math. But, the difference in our ideas is that in yours you have what appears to be a scenario where the user can move in an arbitrary direction, where my scenario was simpler (you can only move from the middle of one tile to the middle of another), which is what I thought the OP had setup.
And no offense but you can use vectors in a 2D RPG as well. Just because you have tiles does not mean everything in the game is tile based. And I'm working on an RTS with someone and I think we are going to use this approach - even with a tile based map. The tiles for the map are simply for rendering purposes - nothing else.