OP is a race realist. By the definition of race realism, OP believes that there are discrete racial boundaries between black people and white people.
"Race realism" is not a clearly defined term with a fixed set parameters. People who believe merely in differences in average intelligence call themselves race realists. There's no reason to believe that these differences commits a person to belief in discrete racial boundaries, just like other differences (e.g. differences in height) commits a person to belief in discrete racial boundaries.
OP believes that the difference in average intelligence is significant and due to genetics. If this premise is true, we can logically conclude that white people have more valuable genes than black people do and are therefore superior.
Having genes better for intelligence doesn't make a group/individual superior. Just like having better genes for height, strength, speed, etc. doesn't make a group/individual superior.
Alt right race realists argue that this superiority justifies atrocities committed by white people against black people.
The alt right has nothing to do with this. I'm talking about your position and your arguments.
Environment can influence intelligence. If a white person is as dumb as a black person because of the environment they grew up in, the white person is still superior to the black person because he is genetically smarter than the black person.
No. Differences in average intelligence does not imply that all white people have better genes for intelligence than black people. There can still be certain black individuals/families/groups that have better genes for intelligence than certain white individuals/families/groups. Just like there can be certain asian individuals/families/groups that have better genes for height than certain white individuals/families/groups, even though asians are on average shorter than whites because of genetics.
There are dogs that seem more intelligent than some humans. However, that dumb human is clearly superior to that smart dog because the human has human genes, which are more valuable than dog genes. Even if a black person won the genetic lottery and a white person got really unlucky, the white person’s life is still more valuable the same way a mentally ill person’s life is more valuable than the smartest chimpanzee.
Dogs/chimpanzees aren't human. Black people are. You still haven't shown that if a race is on average less intelligent, then they therefore belong to a different species.
Some cultures have a caste system, in which those belonging to a higher caste is superior to those belonging to a lower caste.
That's not an argument. Some cultures rape children. So what? I'm talking about your position/arguments. If you're going to claim that "if an individual/group/whatever is genetically more intelligent, then they are therefore superior", then you need to make the argument.
No one says (a) because engineers and janitors belong to the same caste in Western society. In a caste system, (b) is valid.
You've given no argument to suggest that lesser intelligent races ought to belong to an inferior caste system. So saying this is pointless.
A biological classification below the species level would imply that some races are less human than other races. It would spread the concept of “human” into a spectrum. This is a premise of race realism, which OP believes.
Again, there are already bunch of genetic characteristics including skin color can be grouped together (e.g. skin color, height, hair texture, propensity to certain diseases, etc.). Adding intelligence to the already existing list of characteristics changes nothing. Whether you think this counts as different species is something else entirely.
If the differences were biological, then it would suggest that black people and white people are not from the same biological classification.
So what you're saying is that racial differences in hair texture is not influenced biology? You think it's just a social construct?