No, because that new 2014-tumblr-made definition of racism ignores the fact that conception of institutional/systemic racism already exist. And it can be only applied to America/countries with colonial past which created systems to exploit black people.
I don't see how the person you're responding to is using a new definition of racism from Tumblr. Racism isn't just "my race is better than yours". That's a really simplistic view that takes a large issue and diminishes it.
FYI USA and other countries and other colonized areas in Latin America, the Caribbean and Oceania aren't the only ones with institutional racism. It exists anywhere with diversity, which is practically everywhere.
The people saying "black people can be racist!" have adopted a different definition of racism from those that say "black people cannot be racist".
The former sees racism as individual events of prejudice and discrimination while the latter sees racism as a system that oppresses people of color, where black people do not have any power.
That's the point though, they've adopted a different definition, fair enough if you want to call it something different but racism in its meaning is not assigned to one race or leaving any out. I hate how tumblr and SJW's have made up their own definition of it and seem to speak as if it's fact. Reverse racism isn't a thing, because it is just racism, believing your race is superior to another is the actual definition of racism. People want to just label ignorance and whatever else as racism, but it's not the same.
Black and rich celeb: haha racism is dead/rare
like oh ok thanks for your insight I'm sure you deal with lots of everyday/ordinary people, ya'know the kind that kick people out of stores because of their skin.