The video caption on the Daily Motion website says that this giraffe wanted to help out this baby gazelle by removing a branch from its head. The giraffe does remove the branch but the reason is to eat the leaves on the branch. If you look closely at the video the first thing that this giraffe does is to bend down and eat a leaf even while the branch is on the head of this gazelle. The giraffe then lifts it up with its tongue wrapped around the branch. The motivation is to eat and it is not, in my opinion, altruistic. This is far more likely as it fits the motivations of wild animals.
Two useful tags. Click either to see the articles: Speciesism - 'them and us' | Cruelty - always shameful