Is this primary election only for Republicans?

No. It's a foregone conclusion that Obama will get the Democratic nomination, since he doesn't have any challengers (you've got to be even more unpopular than Obama is to face challengers in the primary for your own party when you're the incumbent).

The other parties will have their own primaries. The only one that's likely to be significant is the Republican candidate; but all the minor parties (Green, Libertarian, American, etc.) will be having their own primaries as well.