.nc does not mean much but .vx is a commonly seen video format on the DS (part of the actimagine/mobiclip stuff). Sometimes devs will put an additional extension on files to indicate compression or something it needs to indicate (possibly not compressed in this case -- compression will not do much good on video files like this).
I don't know if we have a working decoder these days as some people were finally looking at it but if you just want to rip them to view on your own time or something then it is probably easier to use an emulator and record that. Looks like there is one saying opening_video.vx.nc so you can probably overwrite that with whatever other files you have there and rebuild the ROM if said videos are rarely seen in the game, or will require hours to play to get to.