My personal definition of racism, as distinct from prejudice or bigotry, is "the desire to harm or otherwise disadvantage others on the basis of race".
I would also define "hate" as needing an element of "desire to harm", rather than the current usage which regards a simple lack of desire to associate with members of a group as "hate".
I like your definition much better— that much better captures both what the term should mean and how it is used (as a pejorative).