The line is either straight or curved. If it's curved.. it curves. If you're asking about whether or not it curves, you ask it if 'does' curve as the act of curving is, well, an act (verb). You could even ask: is the line straight or curved? Or separate it into two questions, maybe: Is the line straight? Does the line curve? (Note: technically, it's not a line if it curves: it's a curve).

Although it is natural to use that form of words, I think it is a question of style rather than grammar. All of these sentences are correct: a) "Is this a straight line or is it curved?" b) "Does this line go straight, or does it curve?" c) "Does this line go straight, or is it curved?" d) "Is this a straight line, or is it a curve?" e) "Does this line go straight, or is it a curve?" .... and many more. The best reason I can give for the choice of words in your example is that, just possibly, we think that a line (or a road or a path) is naturally straight, and that curving is something that it actively does instead of going straight. So we frequently say that "the road curves" instead of "the road is curved." Similarly, we frequently say "the road forks" instead of "the road has a fork."