I would direct him to a scene or two in Final Fantasy XII but, that would rely on the hope that he doesn't say something like 'that game is using movies to tell a story' or something along those lines. I'd probably use Final Fantasy XII over the others because it would come off as more mature (assuming your dad can only appreciate more 'mature' things). Otherwise I'd recommend X, VII, VIII. But X and XII mostly use movies to tell the story anyway so you have to hope he doesn't try and use that defence. Although he can't deny it's all in a game 
Something like The Curse of Monkey Island would be pretty good. But games like Portal, Okami, Monkey Island games have a different kind of story telling. Especially Portal which is extremely subtle in the way it tells its story which he might not really get (I don't even get what's so amazing about the 'story telling' in the game because to me it doesn't really have much of a story.....)
I think Half Life 2 would be good. (although it is a shooter.)
Good luck with it all.
EDIT: like the person above says, Heavy Rain might be a good idea. It tells a story in a way that he can probably relate to using QTE so technically it's all done using gameplay.
EDIT2: I just realise you said PS2, PC, Xbox 360.
I'd just go with Final Fantasy XII. Or X if you think he'd be willing to give it a go. If he says it uses movies you can just tell him it's all in a game and technically you win the argument. Of course don't tell him about the movie thing and hope he doesn't say anything about it.
People say ICO and Shadow of the Colossus are great examples of storytelling in games. I haven't played them but they seem like they're quite good for the most part (although people say Portal is great for storytelling which I don't particularly agree with. It's subtle and works fine but, I wouldn't call it 'great' or a shining beacon in video game storytelling history.)
Something like The Curse of Monkey Island would be pretty good. But games like Portal, Okami, Monkey Island games have a different kind of story telling. Especially Portal which is extremely subtle in the way it tells its story which he might not really get (I don't even get what's so amazing about the 'story telling' in the game because to me it doesn't really have much of a story.....)
I think Half Life 2 would be good. (although it is a shooter.)
Good luck with it all.
EDIT: like the person above says, Heavy Rain might be a good idea. It tells a story in a way that he can probably relate to using QTE so technically it's all done using gameplay.
EDIT2: I just realise you said PS2, PC, Xbox 360.
I'd just go with Final Fantasy XII. Or X if you think he'd be willing to give it a go. If he says it uses movies you can just tell him it's all in a game and technically you win the argument. Of course don't tell him about the movie thing and hope he doesn't say anything about it.
People say ICO and Shadow of the Colossus are great examples of storytelling in games. I haven't played them but they seem like they're quite good for the most part (although people say Portal is great for storytelling which I don't particularly agree with. It's subtle and works fine but, I wouldn't call it 'great' or a shining beacon in video game storytelling history.)