Member function pointers and member functions in C++ are two different things. Member function pointers are not OOP. They are data abstraction.
The entire point of OOP is to make contracts with the compiler that forcibly tie certain things together that are not tied together with data abstraction. Member functions are subject to inheritance and polymorphism. Member function pointers are not. Changing the type of your class will never magically change the contents of a member function pointer, but it will change the constants of a non-virtual member function. A member function will have a this pointer to refer to the class. A member function pointer does not unless you explicitly add one (named something other than this in C++).
Ìf you do it, it can still be OOP, its just not in an OO language. People have trouble separating using a paradigm and using a language focused on the paradigm, for some reason.
The entire point of OOP in every OOP language that I have ever used has been to have the language try to constrain what you can do by pushing restrictions on syntactic sugar involving objects, inheritance and encapsulation, so I would say yes. The marketing claims that people will be more productive at programming by using these.
Yes, you need to have that to have an OOP language. OOP is object-oriented _Programming_, it's about how you program, not what features the language has.
In hindsight, I had your remark confused with another remark insisting that struct inode_operations is a vtable, despite it having what would be static member functions in C++, which are never in vtables, and there being no inheritance hierarchy. If you are disciplined enough to do what you said, then I could see that as being OOP, but the context here is of something that is not OOP and only happens to overlap with it. The article mentions file_operations, but ignores that it has what would be a static member function in C++ in the form of ->check_flags(), which is never in a vtable.
I'm also thinking that these kind of vtables in the linux kernel are what would be implemented by the compiler in C++. But because its self-written, you can be much more creative and do other things, that weren't possible if this would be created by a compiler.
Of course you could implement the same in C++ and then it can't be the same as the vtable introduced by the compiler, so you would just end up with to vtables, you own and the one introduced by the compiler.
The entire point of OOP is to make contracts with the compiler that forcibly tie certain things together that are not tied together with data abstraction. Member functions are subject to inheritance and polymorphism. Member function pointers are not. Changing the type of your class will never magically change the contents of a member function pointer, but it will change the constants of a non-virtual member function. A member function will have a this pointer to refer to the class. A member function pointer does not unless you explicitly add one (named something other than this in C++).