I've had radishes turn viney like that when they go to flower. In my
experience, it is more likely to happen to spring planted radishes that bolt before they have a chance to develop a big root. When you do pull it, you will probably see a stringy, fat root that has very little resemblance to a good eating radish.
Save the seeds on it and plant them around Labor Day and see what you get. If it is a daikon, you might get an impressive root before winter really sets in on you.