This gameplay mechanic is related to dialogue trees, moral decisions, and quick-time events. Unlike quick-time events, however, failure to respond in time does not result in death or repeated attempts, but the game still continues with the plot affected in some way, whether this means the plot branching towards a different ending or the character relationships being affected. In other words, these are moral decisions or dialogue conversations that force the player to respond or make choices in real-time, in order to add more urgency to the decision-making process. In addition, it makes conversations more believable than having non-player characters stand around in silence while waiting for the player character to respond.
Early traces of this mechanic dates as far back as the laserdisc game Time Gal. While it had quick-time events much like Dragon's Lair, Time Gal differentiated itself with moments where a list of choices appear and the player is given a time limit to respond. However, the wrong choices resulted in a variety of different comical death sequences (and then repeated attempts) rather than letting the player continue along with that choice.
This type of gameplay mechanic was largely pioneered by Sega's Sakura Wars series of tactical role-playing / adventure visual novel games, which were very popular in Japan. In these games, this mechanic was known as the LIPS (Live Interactive Picture System) system. The original Sakura Wars presented the player with options to choose from during conversations and events, where the player must make a choice within a certain time limit, or choose not to respond at all by not making a choice within that time. Choices made, including not having made a decision at all, adds or deducts "trust points" from the characters involved. These points have various effects throughout the game, including shaping the player's relationship with the rest of the cast, affecting their performance in battle, and ultimately, deciding the ending.
More recent games to use such a mechanic emphasizing real-time decisions include the FREE adventures games Indigo Prophecy and Heavy Rain, the real-time action role-playing game Alpha Protocol which was also published by Sega, and particularly the point & click adventure / visual novel game The Walking Dead, which became a mainstream success and may have helped this gameplay mechanic gain wider exposure outside of Japan.
The Sakura Wars sequels developed several variations of this mechanic. For example, Sakura Wars 3 introduced an "analog LIPS" system where the player can use the analog stick to determine the force of a response, such as the volume of a shout.
A more recent variation of this mechanic can be seen in the visual novel game Tiger & Bunny, where timed decisions are presented in the form of a talking battle system, where the player must outsmart opponents through dialogues, with certain choices (or lack of choice if the timer runs out) affecting the player's stamina gauge.