A couple of questions.
First, did Mr. Walton get what he wanted out of the exchange?
My answer is YES! Take a look at the demeanor of the player, and their responsiveness to what the referee was saying. It did not matter if there was a yellow, red, green, purple, or no card over the players head. THE MESSAGE GOT ACROSS.
Second, Did Mr. Mutch receive a yellow card?
My answer is NO! Ask me 40 or so years ago and my answer is yes, but in today's game, the answer is no.
Take a look at Law 12 under "Cautionable Offenses", it states in part "A player is cautioned and shown the yellow card if ..." (emphasis is mine). See also p.54 etc in the Advice to Referees. Please note this is true "DURING A MATCH." This changes a bit before and after the match. A good delineation of what a card means and when can be read from the LOTG, Advice, and here (memo on misconduct and display of cards that is on point).
Some time ago a player would know by getting written up in the referees "book." This gave way to the term "booked" that is still used today regarding misconduct. This was the general practice until around 1968 when Sir Ken Aston created them (as the story goes) slowing at a stop light that turned yellow, then red. From there the funny colored cards were used for the first time in the 1970 World Cup. Before that time, no such device was used, only "the book."
In today's game a more obvious display to put a player on notice is needed. I would opine this is true, not for the player themselves, but rather for those watching as if the referee is doing their job right, the player should know from the referee where they stand without the display of a colored piece of plastic.