It just means that you don't own the software that you run. Always having to have an account and sign in and pay the subscription tax otherwise you lose access to it. Now with games becoming digital, if you break their 'terms of service' they can lock and ban your account; taking your 'digital' games away or even locking the console. (Unless you paid for the physical version.)
Arguably this goes for all proprietary software. You're allowed to use software that you paid a license for, but you were never allowed to make and distribute copies of it.
For most practical purposes, licensed software that runs on your computer feels like ownership. After all, we're not allowed to make and distribute copies of published books but we're pretty comfortable saying that we own a book that we've bought. But those copyright limitations are still there. You can own a physical copy of the book, but there are some things you're not allowed to do with it.
Owning a subscription to online software as a service points to the limitations of what we mean by ownership.