The definition of race is all about how you split those hairs. According to the FBI (and most U.S. agencies) you are correct. But then Jew isn't a race either, as it simply denotes religious affiliation and you won't see Jew as an option besides white.

Of course we don't have to split them at all genetically there simply isn't a significant enough difference between the "races" to separate them. So depending on how you define race there's either only one or no races at all.

But that's not how we define it, our culture embraces "tribal" like identifiers based largely on skin color. However race in other countries can be defined in different terms. In the UK and most of Europe for example it falls under lines nationality (these can associate with color but don't necessarily,) in Africa it can come down to actual descent and tribal affiliations, in Asia it breaks into national and then into smaller regional heritage in some instances. Racism, as we know the concept, also changes from culture to culture. In India, at least post-Mughal, it seems to have fallen along religious and class lines.

The concept of race being so flimsy the idea of racism (or at least the practice) is even flimsier when examined from a global perspective.