Are games a good way to tell a story? Should they do it for starters?
I think games can be a good way to tell stories. Different from books and movies, who are passive experiences, while games allow you to be part of the happenings. In fact, games have the potential to be more deep experiences than passive medias. In a book or movies, it is always about someone else. Their feelings, experiences, decisions and their consequences. In games, it could be all about the player.
The problem is that most stories told by games are either skin deep at best. Very few titles have engaging stories, and even fewer have the power to make a deep effect at the player. Games just started to give any importance on storytelling in the last two decades and professional writers only come into play in the last decade. Before, an story was more an excuse for the game design. Today developers are starting to design the game around the story.
One of the main problems of storytelling in game is how to do it without taking away player control. The worst thing a game can do is take away the ability of the player to interact with it. Long cut-scenes or dialogues are immersion breaking and take the main reason someone buy a game. To play it. Some developers try to solve this problem with the stupid quick time events, a dreaded design decision that most players despise. Press X at the right time during the cut scene or game over. Horrible.
Others use the 'walk with me' way. You met the character and follow him while he explain the situation. FPS do it most. Also we have the 'brief/debrief' way. Met character, short explanation, do mission, short consequences scene. Rockstar do it in GTA and Red Dead Redemption.
All of that fail in one aspect: they aren't fun to do and have no real consequences or interaction. My suggestion (I am no game designer, so I may be speaking out of my ass here) is to use more triggered events in games cut-scenes. For example, you are in a library, while one character explain the situation. Instead of removing control of the player, allow him to interact with the scene. Pressing a button near the speaker will trigger a more detailed explanation, or him repeating what he said. Or searching the books could make you find a clue or reference you will need later.
By making the scene the most interactive possible, you can get the player more interested in the story and not break immersion. After all, it is better to let the player toy around than him skipping all unnecessary long cutscenes. Or hating you because they failed to press X at that moment.