I'm actually not seeing anything in the instructions for the experimental one-finger mode for drag and drop so it may not be supported in that tracking mode. Have you tried some of the other control schemes to see if you're able to get drag and drop working?
The description in the AirInput settings for some control modes don't mention drag and drop functionality so you may need to choose one that supports it like Palm Mode or Thumb Mode. The modes other than the two I just mentioned are experiemtnal and may not be a s polished so I would probably recommend using either of these modes for the best experience. Definitely play around with all modes and choose the one that is most comfortable and consistent for you.