You have mixed up two opposing arguments and gotten them blended together.

You have to argue against this dictionary definition. There is exactly zero doubt about this. It is just a consequence of what the words mean (you can look up the definitions in the dictionary, if you have any doubt).

The critical word is typically. Very importantly, the word is typically and not always. The difference between something that is "typical" and something that is "always" is that typical things have exceptions. They are atypical, but they happen. Otherwise you don't use "typically". For instance, you don't say, "typically, red light is a longer wavelength than green light", or "typically, $100 is more than $50", or "typically, a person's hand is smaller than the whole person including their hand". These things are all always true. You say things like, "Typically, vans are larger than cars", or "typically, men are taller than women", or "typically, dogs won't bite you".

Therefore, the definition necessarily says there are exceptions, that is, that there are cases where the target is neither minority nor marginalized. In this country, there is only one group that is neither minority nor marginalized: white people. So it has to be possible to be racist against white people as per the definition. It might be rare, but it has to be possible given the wording of the definition.

Because the definition does not specify why someone is prejudiced against or antagonistic towards the person, any black person who exhibits antagonism towards white people for being white (note--this is possible to find on Medium, and you only need a single case to prove possibility) is, by this definition, racist.

Furthermore, there is nothing in the definition to rule out the person of prejudice being a minority or marginalized themselves, so black people who are prejudiced against other minorities or marginalized groups (or even other black people--that's not ruled out by the definition either!) are also racist by these definitions. The existence of multiple hate crimes in Los Angeles perpetrated by blacks against Hispanics provides the necessary proof of this category of racism.

So the definition is exactly not what you want to claim.

Your task is to argue that these definitions are wrong. Maybe they're oversimplified, or missing historical context, or maybe they reflect a usage that is so problematic that it has to be changed, or something.

But the definitions specifically allow for blacks being racist to minorities and marginalized groups, and also specifically allow for racism against whites.

If you want to argue that dictionaries have got it wrong with respect to their definitions, this article gives you some ammunition: https://www.theatlantic.com/ideas/archive/2020/06/dictionary-definition-racism-has-change/613324/

Personally, I don't think the arguments are strong enough in that article to say that you should remove definitions, but it at least makes a good case that you should add some to reflect more recent usage. You would need to argue that the definitions you quoted should be removed; otherwise it would remain correct to say that black people can be racist. But the Atlantic article at least gives you a head start.