I would agree with you that the theme of this story is race and the way that race is constructed and perceived by society. (There is, I think, also an element of commentary on attitudes towards gender and class.) It is very interesting that London wrote this story given that he is seen as something of a racist himself. You would certainly not get that idea from this story.
The central point of this story is that people (both the people who live in Hawaii and the mainlanders) are bigoted. Because Stephen Knight is not pure white, he is not good enough to be a potential mate for Dorothy. It is okay for him to show her around the islands, but the idea of them marrying would be out of the question. London seems to be saying that this is a bad thing since he has us sympathize with Dorothy as she comes to realize this truth.
There is also a bit of gender and class here. We are told that Mr. Cleghorn has married a Hawaiian and yet is accepted in the best of society. This could be partly because in this case it is the man who is white and that is more acceptable. It could also be in part a comment by London (who was a socialist) on the idea that a high class non-white (she is from the line of King Kamehameha) was seen as more acceptable than a commoner.
But that is just a side note. The real point of this story is that there is this unfair and racist attitude among people.