I don't think this is a cipher. At any rate, if it is it's sufficiently constrained that I don't think it can be conveying very much actual information. Observe:
It's almost a knight's tour. More precisely, it's two chains of knight's moves A-X and Z-A-Y; outside the chains we have digits 0-9, a Y, a Z, and two dots.
It's not clear to me exactly what's going on here -- perhaps it was meant to produce a knight's tour but didn't quite work out, or perhaps the idea was going to be that something is somehow encoded by the choice of squares that aren't part of a chain, or something.
At any rate, I reckon your grandfather was experimenting with knights' tours; maybe something more subtle than that is happening in this diagram (e.g., maybe some information is encoded in the choice of omitted squares), but it's not obvious to me whether that's so.