It’s clear when you see the picture of the cat in the article that the cat has none of these concerns.
I’d consider this to be a form of meditation - still containing ideas of “this, not that”.
Something that has felt much more rewarding to me is to really just exist, but without any ideas of being present, or things you must do or not do. I just sit and take a break from doing anything on purpose. My mind might wander, or it might not. When it does “wander”, and I realize that it’s been wandering it almost feels like a miracle - how is this thing doing this on its own? But that’s not really the point either. Whatever is here now, is here now, whether you notice it or not. And by the time you notice it, it’s gone. So what difference is there between thinking and not thinking?