Your understanding of Democrats' definition of "black" is quite correct. Otherwise, many Democrats/Leftists would be properly identified as the formal definition of someone who is totally consumed with "race".
From the Houghton Mifflin Co. dictionary:
Racist: One who believes that race accounts for differences in human character or ability.
My definition of racism is in my sig.
If we could get a conservative black elected as President it would destroy the Democratic party permanently as their vile ideology became understood by every American.