In this video the baby impala does not seem to be exhibiting the classic fear responses of Fight, Flight or Freeze.
Which fear response is this?
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It's probably not a fear response. Young animals (and human children) sometimes lack it in some contexts. See the controversy with the fear of snakes in children.
Looking at a two similar videos lioness vs impala calf of young lion vs oryx calf however, besides some moments of confusion of the calfs, they do one of two things: face the predator head on (which would work if they had grown horns) or try to suddenly sprint away, which is again not easy for the them to pull off being so young.
So it is a mixture of fight, flight, and probably some confusion as well. There's this notion of learned helplessness but it's a bit of stretch to apply it to any of those videos, in my opinion.
The linked Youtube Video is unavailable but looking at the videos linked by @Fizz it looks like it is a Fawn response. It is one kind of fear response where the stressed individual chooses to be complient with the threatening agent. It is comparable to Stockholm syndrome.
I've read many internet articles on Fawn response in human but I did not found scientific records about fawn response in other animals though.