The nVidia Shield K1 does not have normal file access. You have to download an app called ES File Explorer (I think) to access files. It is much easier to do as Labroides says and use the SD card.
Then you've got far bigger problems than a few lost videos. In any event, you don't get the full quality stored on the tablet, if you are shooting 4K, then the copy on the tablet is only 720p.
Only streamed videos that you see on-screen while piloting the drone are saved on the tablet
And they're not at full resolution and quality as the ones on the sd card(that's in the drone) are
They're something like "preview" videos
You can access the videos through the app but they can't be watched in landscape orientation
Portrait only