What's a non-allelic gene?
It is my understanding that a non-allelic gene is one that affects another's traits, but is not as a typical dominant / recessive manner. If I am correct, this is the same thing as  epistasis - meaning that one gene modifies how another is expressed.
There exists epistatic genes for horse coat color. One gene is the coat color itself (horses may have either brown or red color alleles at this loci), the second gene is for a protein that allows the coat color gene to be expressed. 
For example, a horse has two brown alleles at the coat color locus. It also has a wild type gene in the second (modifier) position. This modifier allows the color brown to be expressed and the horse is brown.
B/B, wt/wt --> Brown
If the horse has the two brown alleles, but has a mutant allele at the modifier position, then coat color is not expressed and the horse is white.
B/B, mt/mt --> white

Because the modifier alleles are separate genes from the coat color alleles, the two are non-allelic - yet they both affect the same trait in some way.

I hope this helps.