The game mechanic where the player is prompted to press a certain button during an otherwise non-interactive scene is called a Quick-Time Event or QTE.
From the point of view of a game designer, it is a two-edged sword.
On the one hand, it is an effective and very simple to implement tool to keep the player engaged during cutscenes and give them something to do during an otherwise non-interactive part of the game. But on the other hand they are a quite dull game mechanic which could often be replaced with a much more exciting and interactive one and can distract from the cutscene instead of adding immersion.
Your first example (the Game of Thrones one) is not a bad use of QTEs in my opinion. By prompting the player to trigger the execution of a character action, the player is engaged in a cutscene which would otherwise be completely non-interactive. I haven't played that game and the video doesn't tell me if the player has the option to not make their character hit the NPC, but it would definitely be a better option when they could because it would give agency to the player.
The second example (Mass Effect 2) is a bit controversial. It is often not obvious for the player what their character will do when they follow the instructions presented on the screen and what will happen instead when they don't. So the red icon flashes in the lower-left corner. What happens when I press the left mouse-button? Will my character shout at the other character? Will she punch them? Will she kill them? The player can't know, and just has seconds to decide. And that in a game where each of the players decisions can have far-reaching consequences. The uncertainty about what decision is to be made right now combined with adding time pressure can make the player feel like they are tricked into performing some action they neither intended to do nor had to do to progress.
Finally, the third example (Kings Quest) appears to be a quite bad use of QTEs. Again, I haven't played the game, but the video gives me the impression that the player has to press the keys showed on the GUI within a very short time limit or they lose the game. Such "quickly press X to not die" quick-time events force the player to focus their attention on the GUI icons which appear on their screen instead of the animation of the cutscene. So they are rather a distraction than adding to the immersion.
Game critics often consider QTEs as a cheap cop-out for adding some action to a games narrative which would be far more fun when represented with proper game mechanics. For example, when you want the player to beat the main villain in hand-to-hand combat, you could implement a proper hand-to-hand combat mechanic where the player can perform different actions and an AI which reacts to them appropriately, but that would be quite a lot of work to polish until it is balanced and fun. Just having a fully-scripted cutscene where the player presses buttons at the right time is far easier. It's also far less fun to play, but it looks almost the same in the trailer when you play it without the GUI. And the reviewers will call you out on taking this obvious shortcut too often.
