I would like to know this too!
My question as well.
Try logging out and logging back in ... you should see the new Todoist layout.
As far as I can see, Todoist Next is the marketing name for the new major version of Todoist.
The team releases new versions of the apps regularly, this is "just" a bigger update, done on all platforms at the same time.
As a Premium user of Todoist, you are already a Premium user of Todoist Next.
If you are using a mobile app, you can just go to your app store and upgrade; I just received a notification, I was using version 2.1 of the Android app, and a 3.0 version has just appeared.
If you are using the web site, forcing a reload of all resources can generally be achieved by pressing the Ctrl + F5 key combination. After that, you can visit https://todoist.com/ and it should automatically load the new version.
If this does not work, to logging out of Todoist, close your browser, start your browser again, log back in.
In case you have bookmarks, make sure they do not contain the app version (part of the URL are such as v=199 or v=202). Either create a bookmark to https://todoist.com/ directly, or recreate your bookmarks.
So what's the stuff on visual scheduling about? I tried to watch the video, but couldn't, so is it just the same functionality we've always had or something new?
'Visual scheduling' = icons for 'single click' selection of 'Today', 'Tomorrow', 'Next Week' or 'In one month'. No, it is not a calendar nor a GANTT chart.
That's a shame! I've been hoping for that for a while. Thanks for confirming though.