I see a lot of people betting on game streaming but I'm pretty certain that's not the way we're going to go.
1. Console sales are still on the up. The market is clearly not saturated for traditional gaming consoles.
2. Game streaming services already exist and 3. These services continue to be in a niche position. Save for a few enthousiasts, they haven't caught on in years.
3. Games are like books, content that is just not suitable for streaming. Music and movies lend themselves well to the mentality to having a vast collection of media to consume on a whim and in a moment. Books and games are something you put significantly more time investment in and thus are better to have in a personal library. Books, like games, have streaming services and just like games, these aren't mainstream despite having existed for years.
So no, game streaming is not going to be a major thing. But what do I know, I listen to music on vinyl, I might just be resistant to change.
I reckon this is why people see console gaming moving to mobile. That technology gap is shrinking and it offers a bigger difference to PC gaming.
But it's not going to. Mobile gaming and console gaming are two totally different markets. People who occasionally play a game might do so on their smartphone (as was done on GSM's in the past). No one is going to say "my smartphone is good enough, guess I don't need a console".
So no, the mobile gaming and console gaming markets will continue to exist next to each other.