Seems to me you can hear the wind at points on the video. A windsock is not necesarilly a good indicator for very localized gusts. On floats one often has only the water to read and airplane behavior to read to make quick decisions. Not many windsocks away from "civilization". Interesting info above regarding the possibility the pilot had been recently checked out in the Beaver, don't know veracity of that, but the Beaver, like anything, can be kinda squirrely in crosswinds. Looks to me like the float bows are pretty high during the take-off, almost like plowing instead of fully on step. With the nose high, less of the floats' length tracking through the water, and high power (p-factor), the Beaver will definately want to turn left on you. A good thing to check on Beavers on floats is that you are getting full air rudder travel, ie that the air rudder travel is not limited by the water rudders' rigging. Cables stretch over time and lose tension too, especially when rigged to water rudders and their associated tensions.

Glad the pilot and passengers are okay. The Beaver can, and probably will be re-built.

Stay safe.