Except that their view has nothing to do with "race" or ethnicity or heredity. It's a sense of entitlement to rule that is based on religion . Anybody who wants to can join simply by converting.
This is very different from the Spartan or Nazi view of things, where you have to be born into the "master race." You can't join up.
From a purely practical standpoint, a "master group" you can join is likely to defeat one based on heredity. Getting lots of your potential opponents to join your side makes a lot of sense. The Romans were really good at this, a major reason they conquered and ruled more of the ancient world than anybody else.
Really I think it's over the top to associate "master race" ideology with Sparta. Sure, Spartans fought their share of wars, as all the Greek city states did. But I've never heard of them setting out to genocide another race in total.