Are pilots generally trained for crosswind landings?
Of course yes.

Crosswind landings, like the one in the video you linked, are very common. In fact, landings with no wind or only headwind are rare.

There are several techniques pilots are taught during their extensive training to land aircraft when there is crosswind. The Wikipedia article I referenced above lists them. Since your question isn't about them, we won't discuss them.

Certainly, extreme weather situation are not very common. Some parts of the world experience extreme weather more than other areas. Diverting to other airports is not always an option and in some cases, once an airplane is on the approach, going around becomes impossible.