That was a yellow card (also audible: warning for misconduct)! A red card would indeed been harsh. Here's a better video of the incident: (Disregard title, description, and YouTube comments on that video. Sadly, the understanding of Badminton laws by many YouTube commenters tends to be incomplete.) Also, note that we don't see the whole match. Usually, a yellow card for delaying is preceded by multiple verbal warnings - although in this case, the delay would imho justify a yellow card even if the prior behavior was spotless. It's not like the laws are vague on this point: I don't think anyone would argue that 20s+ pauses between rallies constitute continuous play. The amount of theater and complaining to the line judge is unjustified. Both delay and unsportsmanlike conduct could justify a yellow card on their own. Taken together it seems like a textbook case to me, doubly so if Sayaka Takahashi had been warned previously for delay. And in most cases, a yellow card's effect is literally symbolic only. In fact, most likely Sayaka Takahashi didn't even incur a financial penalty, since at international tournaments you only have to pay once you reach three yellow cards in a year.
Here is a better video: In the very first second, we see Chris Langridge talking to the umpire already during the warmup. Just before he sees the red card (just after warmup), he talks to the umpire again. After the referee comes on court, they test the shuttles (2:32), so I think it's very likely that Chris Langridge complained about the shuttle. Of course, a normal complaint will not even warrant a yellow card. My hypothesis is that the language used was not befitting sportsmanlike conduct. The shuttles seem to be too fast indeed, but the referee arranges for a different shuttle speed.
Yes, yellow, red and black cards are given to a specific player who has to pay the fine afterwards, but all other effects are to the side (=doubles pair). Quote the RTTO (emphasis mine):
Thanks, that shows the whole history. As I wrote above, I think the yellow card is completely justified even without any context. Watching the whole game, you'll see After 4 verbal warnings, the umpire must escalate if the behavior does not improve, even if the behavior would not be card-worthy on its own - in fact, an earlier yellow card would certainly be justified as well given that history.