Today we understand that that kind of stereotyping is a universal attribute of human cognition and therefore not explanatory. That is, you can't get from that definition of "racism" to the society we see around us today. Every human does it--everyone is "racist" by that definition--yes, including black people. And yet black people are still far worse off, on average, than whites in American society.
So that definition of racism is useless. It doesn't explain why things are the way they are, and we can't change the way our brain works at such a fundamental level anyway. It has even become a joke--see Stephen Colbert's riffs on "I don't see color."
So yes, the concept of racism has evolved to include power. Without power, stereotypes don't have an opportunity to cause actual harm. You have to consider power to understand why American society, on average, treats white people and black people so differently.
It's probably better if people used "structural racism" to define what you mean here. Similar to how "sex" retained the original definition of sex, and "gender" was used for the social construct. If people tried to say "There is no such thing as being born with a binary sex, because sex is a social construct" then it would be equally confusing.