[UPDATE]
According to preliminary poll results, lots of people think that indeed there won't be a 9th generation.
Personally I think that there will be one last generation, but only under the form of a Game/Streaming box, since the internet infrastructure but also streaming technologies (have you looked at webM on Neogaf?) will be largely sufficient by then.
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This is pretty historical (for video games):

Consoles are reaching the limit of their relevancy with the always developing laptops, mobile, integrated GPUs, or rendering/computing technologies and cloud computing, the point of having a big box with a fixed hardware next to a TV that is even slimmer is getting away.

Microsoft didn't lie about their cloud-powered games and there are reports from Microsoft about leaving Xbox as a console platform, while Sony released PlaystationTV and more importantly, PlaystationNow-ready Sony TVs.

And you didn't need to wait for them to make a guess, Steam, Origin, Humble Bundle and other such services, as well as Ouya, SteamBox, ChromeCast or AppleTV have all been indicators that the future of console is just a smartTV connected to cloud video game service.
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Before asking you what do you think it will change, not only for the way the 8th will unravel but also the future after, here are my though on what it means and will happen:

• Sony's Playstation, Microsoft's Xbox, Valve's Steam, Apple iOS or Nintendo will become Video Game ecosystems, like dedicated cloud OS services.
• The first strategic key will be the hardware it is available or locked on: TV, Tablets, Laptop, Browser etc...
• These hardware are barely screens, interfaces and operators . But the ever-evolving server side computing technology at play will be what make a difference in term of power.
• The second strategic key is what these services offer in interface, quality, price and catalogue, pretty much like you chose Netflix, Hulu, Spotify or Pandora.
• Another interesting strategic key will be the new experience provided, wether on the hardware side with VR headset or software side with the specific engines and computing technologies developed for each or several platform.
  

What will it mean for games?
Will there be only indie or poorly developed F2P games available on a specific platform like on iOS, or crazy millions budget AAA titles promoted on each services from which you'll just choose ease, option or price?
Will it mean that the PC will eventually win all, or rather that Playstation will come competing with Steam right on the same platform, and that the Sony cloud technology will compete with your Nvidia Card (when they'll both be able to flawlessly stream 1080p/60fps webM)?

I don't think so. I feel like if anything consoles will first become digital only but I still think that's a big maybe, I think at least for now physical media is here to stay.

Streaming is also less reliable than digital because with streaming you always require a constant connection where as digital you usually just need enough time to download the game. So I don't think risking backlash from fans the console manufacturers will do it. However I do think that as a whole the digital and streaming markets for video games by next gen will be much bigger than they are now but not enough to replace the status quo.

Nope, the internet infrastructure will not be good enough for streaming games for a few decades.

There will always be consoles as long as people buy them.

What you have laid out is a very good possability going forward. I was thinking that PS4 becoming a dual boot Steam machine would only be good news for both companies.

I don't think we will see the transition happen fast enough to make this the last console generation, but I do see streaming and service based games being the future.

I am still hoping for more multi-tasking, 4K/60fps, and VR to be fully worked out in a PS5. Also, I think physical consoles will continue a little while longer due to worldwide restrictions. Super populated places are nearly ready to make the leap, but even in the outskirts of big countries internet is not up to the snuff, and won't be for some time.

I think that VR set, along smart TVs will be the main component of choice rather than the console, once you've chosen your platform.