Every Airline has their regulamentations, and I can tell you from friends that fly planes for airlines that every flight plan comes with an alternate airport.

Upon approaching their destination they get weather readings from the controllers and from dispatch. If the weather included a max degree cross wind (I think it's 40+ degrees, but don't quote me on that) it would be up to the pilot to make the choice. If the weather was more than the airplane could handle, the airport would be closed and they would have to choose to get into a holding pattern or to proceed to the alternate.

Considering they got a clearance to land, that means that the weather (even if it looked that bad) was declared within the airplane limits.
The only mistake that I think the pilot did, is that once over the threshold the plane got a big gust and made the plane wobble and lose the centerline by a few feet. At that point there was plenty of time to abort and try in a few minutes.

Another typical regulation is that pilots are given at least 2 attempts to land, if they abort both of them then they are instructed to proceed to the alternate destination.

There is a video out there that shows the max crosslanding performances of a boeing 777 and a boeing 747... very impressive... but no wind gusts there ;)