Immersion is the wrong word to use to define the concept described in TFA.
What is described in TFA is much closer to what is called "The Suspension of Disbelief"
In any game that is telling some sort of story, the objective is to design the game in a way that tells a story. And every good story should draw the "reader" into the imaginative world of the story (Suspension of Disbelief) so that the "reader's" imagination can assist in filling the gaps. Whenever a story includes or excludes certain details (inconsistencies) which cause the "reader" to be jarred out of the imaginative world of the story, it momentarily disrupts the "reader's" imagination.
The best storytelling goes to great lengths to avoid such inconsistencies, while the worst storytelling doesn't care about "Suspension of Disbelief" at all and doesn't bother with trying to remain consistent.
This is true for movies, or novels, and for storied games. It doesn't apply to games that have no story, such as Tetris. So, when a story based game has jarring inconsistencies or is injected with strange pauses while the player is required to complete some weird mini-game that doesn't fit the environment of the rest of the game, it disrupts the fun of the game by disrupting the Suspension of Disbelief.