If they are any of these things, they are a race. We must keep in mind that race is only a social construct, though.
They aren't a religion because they can belong to many different religions. They are not an ethnic group because African Americans can be Spanish-speaking, can come from Africa, or can come from ancestors who have been in North America since the 1600s. This leaves only race. To some extent, African Americans look different from the rest of us. This is the only thing that they truly have in common with one another. Therefore, they can only be called a race if we have to call them one of these things.