Yes of course, but you won't need any extra device (except a controller which you link to your tv or tablet). There will also no need for physical media like cds or dvds or b-rays or anything else, no need for installations (except the app running on your tv or tablet). The backend (streaming service) requires a good amount of high end cluster "pcs". For the manufacturers, like Sony, Microsoft or Nintendo there won't be any need for different devices to run/stream the software.
This progress won't have any conflict to the selling strategies of the manufacturers. There will still be Playstation, Xbox and others. The difference for the customers will be the form of subscription. You'll still stick with Playstation Plus (or Playstation Now, whatever they'll call it), Xbox Gold and whatever they'll bring up.
But it's a huge difference in production of the games. No game ports anymore, no different hardware specs you have to compare from, less testing. They will spare money at the production, they will spare at publishing (no more cutting disks) and they will spare the subsidy for the device.
Don't worry - the market for games won't die - but the whole concept of different devices will disappear.
Edit:
And also don't worry - you'll have fun with your PS4 at least 5 to 8 years. Depends on how fast the market will change.