You can do it with or without AI / navmesh.
What kind of board are we talking about? What kind of movement? There’s probably a dozen ways to approach it all - some may be better than others, depending on what is really needed.
You say it’s not chess. Is it like Monopoly then? Or one of those:
Interconnecting paths? 2d / 3d? Or something completely different?
Also, have a look here for something truly generic:
