By this overly simplistic definition you would count infertile cats as non-cats. You also completely lose the ability to differentiate the species of non-sexually reproducing organisms. And then there's the insanity that is hybridization. Is a mule a horse or a donkey? They can occasionally reproduce with either of them.

this is not the point at all... yes it was an overly simplistic way to explain how you're using the fallacy wrong. You still used it wrong.

In just the same way with economic systems. Workers in different societies and periods exercise different levels of control (which is the underlying meaning of ownership) on the means of production, it's not black and white. It can be very roughly defined as (workers control over the state) * (relative assets of state-controlled enterprises) + (relative assets of co-ops or other directly worker-owned enterprises). There is of course a lot more nuances to be discussed, such as the exact distribution of control between different subclasses of workers, or the social hierarchies arising from the structures of control.

no it cannot because it's referring to whether or not the workers control them and on a societal scale this is a binary flip, at some point the workers are more in control than the bourgoeis and at that point it is socialism and at any point before it is not.