There is no justification for it. The writers are being inconsistent as to whether "battlestar" and "basestar" are proper nouns or common nouns.
The very start of the article establishes ground for some confusion with regard to "basestar." If there were such a thing as "The Basestar" as the one and only "capital ship," then that would be justification for treating The Basestar as a proper noun.
It seems clear to me, however, that basestar is actually a common noun. The fact that there is a capital ship out of all the ships still leaves room for calling that specific one "The Basestar," but ultimately I don't think that line of argumentation holds up. My supposition is that out of all the basestars, the capital ship probably has its very own proper name -- just like each of the battlestars have their own proper names. (I can't remember what they are. One of them is obviously Galactica.)
The answer is that "battlestar" and "basestar" should not be capitalized unless they are used as part of a proper name (Battlestar Galactica or Basestar Something).