She thought he was delaying the game. From ITTF Guide to Match Officials:
13.2.1 The requirement is for play to be continuous throughout a match, apart from authorised
intervals, but if, for example, the ball goes outside the playing area, clearly play cannot
continue until it is returned. The intent of the regulation is to prevent deliberate time-
wasting, such as by repeated bouncing of the ball, long pauses before serving and
prolonged discussions with a doubles partner, which should be firmly discouraged.
Also, the yellow card IS the warning. We cannot tell if she may have given him some verbal warning earlier in the match which we would not see on the video, but in any case, she is not required to do that. It certainly didn't affect the outcome of the match.
17.2.3 When a formal warning has been given, a yellow marker should be placed near the
score indicator, next to the score of the player who has been warned. Similarly if a
player has had a penalty point awarded against him or her, both a yellow and red
marker should be placed near the score indicator, if space permits. If both the umpire
and assistant umpire are using score indicators then the cards should only be placed on
the assistant umpire’s indicator.
These warnings apply for the remainder of the
individual match or, in a team event, the remainder of the team match, and subsequent
offences will incur penalty points.