I mean even if you accept that definition, uh does the mayor of the third largest city in the country not have any power?
I guess so, yes.
However, I think what they're saying is that Black people don't control most institutions of power in the United States (governmental organizations, corporations, courts, banks, schools, churches, media, etc). It has always been white people in the overwhelmingly majority (or all) of those positions and thus they believe that "Black people can't be racist".
I don't agree with that rationale though. They are describing systemic/systematic/institutional racism. Systemic racism is not the only form of racism. ANYONE of any ethnicity or race can be racist.
For example, I have unfortunately seen a few Black people (mostly online) who are racist. I've seen a few Black people online call (East/Southeast) Asian people "ch*nks" and "g**ks", call Latino/Hispanic people "sp*cs" and "w*tbacks", call White people "white devils" and "cave beasts/monkeys" and so on. It's terrible. I have also seen a few Black people both online and in real life who are anti-Semitic/anti-Jewish. They believe that Jewish people "control everything" and are "evil". Some of them also believe that the Holocaust didn't happen or "wasn't as bad as they're saying". There are also a few Black people that believe that "we (Black people) are the real Jews/Israelites" and that white Jewish people are "imposters". It's all disgusting and sickening. Ignorance and racism is not limited to a single ethnicity or race. We, as a society, have to make sure we call out racism no matter where or who it's coming from.