The problem with Taggart's animation during that scene is that it's the stock animation the game uses for all normal (male) NPCs. It's one of the many small details that bothered me in HR. And they look shit. There is a conversation "boss battle" with Taggart later in the game, and for those battles the game uses unique animations that were specifically made for those battles. That's why they work so well, and Taggart moves and behaves like you would expect him to. Immediately afterwards you'll get a follow-up dialogue with him where he is, once again, animated like every other generic NPC. The difference is so jarring, it makes it really difficult to get to like the characters when they all show the same mannerisms.
What is it with animations and facial expressions that's still so difficult today? You mentioned Bloodlines in the video which was released in 2004. The characters in that game are much better animated than in HR (even MD). Sure, the models have fewer polygons, are less detailed and use low-res textures from today's perspective. But the animation and expressions still hold up, and there are no lip-syncing issues. It feels like you are talking to people, not stiff puppets. I don't get it. The Source engine pioneered this over a decade ago. By now, every game should be using this technology or better. Where is the advancement?