Engage wall of text!
The problem with video game stories is that you need to play the game to get to the story, which is a problem because non gamers can't play video games. Any game that is complex enough to prove your point will inevitably be too difficult for him to play. Video games are interactive by their nature and if he is unable to enjoy that interaction he will never appreciate video games. Video games, by their interactive nature, are far deeper and harder to comprehend than a book or movie. You need to earn that comprehension, and he has not.
Right now your dad has a set view point and he is sure you are wrong. He will never accept your argument until you are able to challenge his current perception of reality. You need to convince him of the inherent value of a game vs other media.
1. The first thing to do is tell him that in order to get your point across, you will need some time an hour or so, and you will be able to begin showing why games have value. Explain to him that you need this time because video games have a high barrier to entry because they are often created by different cultures and require highly developed skills to play.
1a. If he challenges this, pick a non violent and simple competitive game and challenge him to compare skills. Geometry wars 2 is great for this. The controls are very simpl, you only need the demo, and it is impossible to miss the point. Explain to him that you are going to prove that games require special skills and challenge him to a match. He will play a 3 minute match, and then you will play a 3 minute match. You will destroy him. Explain that this happened because you are better at games. It works even better if you have never played the game before.
1b. Tell him that you are now going to explain the primary aspect of video games as a game.
2. If your father is a sports nut, that is a really good place to start. Bring up his favorite sport. Lets say for arguments sake it is American football (my father's favorite sport.) Ask him why football is a good sport. He will tell you about teamwork, skill development, complex strategy, etc. Then ask him why watching football is an acceptable pastime. Point out that by watching football he is not reaping the benefits of playing the sport but using all the time that it would take to play the sport. Point out that it is only a game, after all, and really isn't that important.
2a. Challenge him to justify spectating professional sports. This will challenge his current perceptions, opening him to new ideas. Never be aggressive or confrontational and if he gets defensive point out that this is a hypothetical discussion, that you already understand why he values sports. Never attack his favorite things but don't let him derail the conversation.
2b. Next, you should compare video games to sports. Both require skill sets. Both require knowledge, both put us up against difficult challenges and require us to overcome. The primary difference between a video game and a sport is that one is primarily mental and the other is primarily physical.
Tell him to keep this in mind and that you will come back to this, but now you are going to move into the second aspect of video games, interactive story telling.
3. Chances are you have a pile of games around. Choose 3 or 4 out of them that have strong stories. Give your dad a short 1-2 sentence explaining the basic story of each with emphasis on the role of the player in these games. For example:
Bioshock is a game about a man who tried to create a utopian society which then fell under the weight of its own corruption. You explore the ruins of this society, piecing together how it all went so wrong.
Metal Gear Solid 4 is about a soldier who has fought all his life to avert world wide nuclear disaster. You take the role of the aging soldier who hates war in a world where war has become routine and impossible to avoid.
Fallout is about a hypothetical nuclear war that left the earth a desolate wasteland. In this game you take the role of a person struggling for survival in a desolate and cruel world.
Mass Effect is a science fiction space opera, like star wars, where we take the role a man desperately attempting to protect billions from a genocidal alien threat.
Make sure to throw in a few not violent games, such as:
Phoenix Wright, Ace Attorney is a comedy drama where you take the role of an attorney who protects the innocent from false accusations of murder.
You get the idea. pick the games before hand. Explain to him that not all games have this value, but many do.
3a Now tell him that the reason video games have unique narrative value is because they let us experience the story. In a movie we can see Mad Max explore a desolate wasteland, but in Fallout we explore that wasteland ourselves.
4. Show him the opening of one of the strong narrative games you showed him earlier. Make sure it is one with a strong opening cut scene, violence is not glorified, and is not Japanese made unless it is Metal Gear Solid 4. Not Half Life 1, 2, or Portal. Show him only the opening, don't let him get into actual game play.
4a. If you have Bioshock it is a great one to do. Let him control it if it is Bioshock. right up to the point where atlas first calls you on the radio. Don't let him go any further!
4b. Point out music, narrative themes that are introduced, etc.
5. Next, explain that you are going to show him how game designers view games. Explain that the video's you are about to show him were made by videogame designers to show the average joe how video games can have narritive value and why this narritive value is unique to interactive media. Show him these 2 video's.
http://www.escapistmagazine.com/videos/view/extra-credits/1974-Enriching-Lives
http://www.escapistmagazine.com/videos/view/extra-credits/2545-Narrative-Mechanics
Make sure you have them ready to play before this point so you only have to press play and you are in the video. The last thing you want here is an advertisement for duke Nukem to get in the way or for video lag to lessen the impact of these video's.
6. Tell your dad that now that he has the proper background to understand video games and interactive narrative, it is time to play a game. Portal 1 is our game of choice here, and it really needs to be portal 1. He will play the game, if only for a half hour or so. Explain to him that the game is a dark humor science fiction in which the player is in the place of a human lab rat at the mercy of an insane artificial intelligence. Before he starts, tell him that this is a pretty complicated puzzle game and that if he needs any help you would be more than willing. Stay with him while he plays. Show him by example that even a single player game can be a shared experience.
If nothing else, this should help your dad understand the value of interactive narrative. If you want, offer to play games with him, parents like to spend time with their kids.