For me a game is not something that anyone can define or something that you can really place people into categories for. And the reasons that I say this is because if you have 5 people play the same game. You're going to get 5 different opinions about what is happening with the game and how they felt about it. No matter what you call a 'game' it is a going to need a creative base that is going to stem from the creative mind of the first developer making it, and the creativity is infinite. So, even if you think a 'game' is supposed to be a certain way people can make variations of it to change what your core concept could be. I also think that people get the 'Video Game' term and the 'Game' turn completely mixed up. That for instance EyeSpy because you use your eyes it is a physical game obviously, but it also require no mechanical or physical skill. But if you take on the opposite end of the spectrum you have games like Onward which requires intense mechanical and Physical  Skill. So, overall in my opinion I think the entire argument really doesn't make since because Even if you're a game formalist or abstractionist if you realistically look at games that supposedly "fit" in either category they still won't all be the same concept and "fit" the "guidelines" to be in said category. A game is simply like how Art is. It is whatever you make it to be. A "Beauty is in the eye of the beholder." type concept.