Nope. You can't define a term in reference to itself. There are no races except those that racism defines. You therefore cannot treat people differently based on their race without racism being present before the treatment. Therefore, treating people differently based on race cannot be the definition of racism.

Abstract racism, which doesn't really exist except for in apologia, is a system by which we categorize humans into groups by phenotype.

But none of us have ever experienced abstract racism. We all know and have experience with one historical phenomenon called Racism, and that is European Racism. European Racism was developed by the European elite in order to divide humanity into categories that they could use to justify their domination and enlist the non-elite of their society in defending, supporting, and spreading the dominance of those elite.

That racism is the racism Europeans exported all over the world through violent dominance, subjugation, colonialism, and neocolonialism.

Once you understand that, it becomes obvious that we are require to treat people differently based on which racial category our society assigns to them, because the harm they experience from our society is informed by that racial categorization. If you don't treat them differently at all, then you are failing to acknowledge the harm they have experienced and therefore cannot possibly approach justice.

It would be like a doctor saying we can't give people different treatments based on the form of illness they have because that would be a form of unequal treatment.