Why do spoilers seem to be slightly activated during take off? In this video (minutes from 10:46 to 11:00), the spoilers seem to be slightly deployed during take off. What's the purpose of this? I've already seen this in other videos too.

I've also read the answers to the question When can spoilers be used on airliners, but they seem to be related to slowing down the aircraft or for descending faster. But what is the point during take off, when it's supposed the pilots want to climb and go faster?
Spoilers lower lift and increase drag on the side where they are deployed. Symmetric spoiler deployment, therefore, is for slowing down. Asymmetric deployment not only creates a (small) rolling moment, but primarily a yawing moment which helps to counteract the adverse yaw created by ailerons, especially at the high lift coefficient at takeoff and early climb.

Spoiler deployment increases pressure ahead of the spoiler due to the slowing of local flow ahead of the obstruction caused by the spoiler, and it creates a local flow separation at and behind the spoiler, which in turn lowers the local pressure. Only the first effect lowers lift, but both create drag. The main effect of a limited spoiler deflection, therefore, is to increase drag.