Racism is oppression based on racial hierarchy.
Bigots come in all races, but by definition, black people (for example) cannot be racist to a white person.
Some non-white people do "play the race card." However, I'll point out that white people "play the race card" every day of their lives. They may not know it, but they do. Such is the privilege of being white in this country.
The legacy of slavery has benefited every white person in this country—directly and personally. In a very gross analogy, if you run a series of foot races over 300 years but prevent 13 percent of the participants from learning how to run for 180 years and then give them concrete sneakers for another 80 years—but allow them full access for 40 years, it will take the 13 percent quite a few races to be competitive because the other 87 percent advanced their skills by practice and repetition.
Life is not a foot race, but it is a fact that the average white person would not economically benefit from switching places with an average black person (black households average one-tenth the household wealth of white households). If you believe all people are created equal, there has to be a reason for this—and there is: racism.