Yes, genes do influence behavior, although there's a LOT we still don't know in this area. Lab studies with mice (don't laugh, genetics works much the same way in both species, and no-one has huge cat colony studies for behavior!) have even shown that some color genes also influence behavior traits.
We're just in the early days of understanding the genetics of behavior. For one thing, environment (learning, etc.) has such a huge influence it can really cloud the picture.