Meanwhile on Korean TV...
There are many Bollywood movies that are equally bad...
Edit: I just saw the HIMYM episode...
I see the episode more as a homage to old cheesy Kung Fu-movies than anything else.
If the three teachers would have been portrayed by some random white people trying to act Chinese, I may think that the article writer would have a point, but they were actually played by three of the five lead actors, which was a plot point in itself. All people who were supposed to be Asian were played by real Asians.
Also, the three teachers were not in any sequence supposed to look real, but in a colourful story told by one of the characters, and as interpreted by another character according to that second character's imagination. As such, any stereotyping in that story is a reflection of the second's character's own bias. That character is often portrayed in this TV-series as having outmoded prejudice about a lot of things, so it would only make sense if he imagined the three teachers as stereotypes.