My 2 cents:
What you're doing looks good, and nothing is wrong with skidded turns or scarving. I do think some terrain is better for carving than others, while skidding/scarving is more widely useful.
That said, groomed runs/groomed hardpack is really good terrain for carving. If it's too icy, that's not good (since your board will slip), but if it's just a little softer, it can be great for carving.
I think one issue is that when you learn to carve, you have to be patient with the turn. You let the sidecut of board turn you, and you make these gradual S turns. I think when you carve, you get on an edge, get the appropriate balance, and let the sidecut do the turning. You're doing great linking turns, but if you watch your video, you can probably see that your board makes these sharp direction switches. It's like zig-zagging rather than S turns.
Also, it's definitely good to learn to carve on terrain that's easier for you... some kind of run where you can get good speed, and are not afraid to point the board straight downhill. Carving/S-turns, you will need to have your board pointed downhill longer than with skidded turns.... at least until you learn to get faster edge to edge.