What is the intuition behind the form of the hypothesis function for movie ratings?

I'm trying to understand why it makes sense to multiply user factor by movie factor, to get that factor's contribution to the rating. E.g. if user doesn't like horror movies and the movie has a low "horror movie" rating, multiplying these together gives a low number. Shouldn't the rating be based on the distance/difference between a user's value for a factor and a movie's value for that factor?

I understand that in a learning situation the factors do not have specific interpretations -- there is just a list of factors. Still, the motivation was clearly that there are factors (horror-ness, comedy-ness etc). So what is the motivation behind taking the product of factors instead of some form of their difference?