It’s now an illegal move, even in Blitz, under FIDE rules. Even world champions cannot break old habits in time scramble chaos.
Under CCA rules, #20, in Regular and SD events, you are allowed to use two hands to castle, promote, and/or capture pieces. FIDE rules say when making a move only one hand may be used. While we might expect all players to be au fait with all of the rules and which rules are in force, it does get confusing at times. For example, Magnus Carlsen forfeited a game because he forgot which time control was being used.
I am OK with the “one hand” movement rules. When both players are using two hands to move pieces and make captures, the pieces are frequently knocked over causing a mess. It is difficult to tell if the clock is pressed before or after a move is made. The flurry of hands is always a distraction and thereby not acceptable in a serious game of chess. The two hand usage is more frequently seen in Bughouse.
Since the event started in June the new rule was not yet in effect.
Hmm, interesting. The video eventually shows the game close-up enough so that I could see that a 2-second increment was in effect.
A 2-second increment goes hand-in-hand with the new no-two-hands rule. With increment, the players should need only one hand.
I wish we’d stop playing blitz at G/5 d/0 in this country, and adopt the international standard of G/3 inc/2. I, for one, will never play in a d/0 event, blitz or otherwise.
Bill Smythe
Can you still push the pawn with your right hand while picking up the promotion piece with your left hand as long as you then transfer the promotion piece to your right hand so that your right hand can place it on the board and hit the clock?
Contrary to many here, I can find no rules specifying what can and can not be done with captured men (that is pieces and pawns).
Alex Relyea
I’ve seen a couple of women players move the piece and press the clock with their left hand, but write the move with their right hand (or vice versa). Cleverly efficient. So far I don’t think FIDE has disallowed that. I can’t wait for the day when some opponent cries foul.
Bill Smythe
True, but is it relevant? Suppose no captures have been made, a pawn is promoted, the arbiters HAVE provided an extra queen. Does that influence the answer to the question). I doubt it.
I don’t have a rule book handy, but I don’t remember either FIDE or US Chess rules saying anything about which hand you write with – only that you have to move and press the clock with the same hand. As a right-handed player, I generally do everything with that hand, but lately, a painful right rotator cuff has me moving and pressing the clock with the left hand. However, there’s no way I can write legibly with that hand, so I still keep score right-handed. I can’t imagine anyone objecting to that.
Well, I can imagine it, since some players always seem to find something to bellyache about. But as you say, the objection has no merit at all under either FIDE or USCF rules.
Bill Smythe
If you allow use of both hands for castling, captures, or promotion; then do you require the player to push the clock with both hands? 
Larry S. Cohen
Only if you castle with your opponent’s rook.
Bill Smythe