I watched the video and I think I see what you mean about the needles disappearing.
OK, well here is the trick with DPN’s. I’ll try to describe it, although I’m far from an expert!!
You have 3 needles with stitches. You will hold the needles in a triangle, more or less. The needle that has the tail coming off of it will be on the right side. The needle that has the very first cast-on stitch will be on the left side of the triangle. The middle needle will be on the bottom of course.
OK, now forget about maintaining any sort of triangle while you knit the first row, things will be flopping everywhere! You’ll hold the left side of the triangle (the needle with the first cast-on stitch) in your left hand.
Assuming you hold the yarn tail with your left hand normally, go ahead and wrap it around your left hand however you normally would (don’t worry too much about what the needle it’s attached to is doing, it will flop around).
So, in your left hand you should have the yarn and one dpn needle, and they will not be attached to each other in any way.
In your right hand, you want to hold the empty needle.
Insert the empty needle into the first stitch… wrap that floppy yarn tail around it, knit your first stitch and slide it off.
You’ll have stitches on 4 needles now, temporarily. Finish working stitches off of the first needle until there are none left.
At this point, you have stitches on 3 needles again, and the round should be joined, so it should more or less hold its shape.
You can now rotate the triangle and do the same thing with the 2nd needle… insert the empty needle into the first stitch, wrap the tail (which is attached to another needle entirely) around the needle and pull it through.
I hope this helps! The confusing part for me was that the working yarn is coming from the right-hand needle, but you won’t knit onto that needle, you’ll just use the yarn for your stitch.