I'll just go ahead and say the last thing I try to do on super icy surfaces is carve... as soon as I get up on my edge at anything over a minor angle my board just wants to kick out. If the conditions were really bad - it's hard to tell from the video because I do see that decent layer on top, mellow skidded turns might have been the best thing.
Your turn initiations were great, I could just see you weren't leaning very hard into your turns probably due to the icyness. Bad conditions suck and have to be ridden accordingly no matter how good you are, so don't get too discouraged.
PowderHound and TreeNinja