A game usually has to achieve something for someone to like it, so "x is a flawed or good way to achieve y and y is a thing a game should be trying to achieve," is still a conversation you can have. Again, I'm not entirely sure what you're getting at here.
Okay let's try this again, from another angle. Perhaps you've read the Euthyphro? I'll be taking cues from that:
Is the game good because it is liked?
Or is it good because it is likeable?
If the former, the goodness of the game is not about the game itself, rather the person liking the game.
If the latter, the goodness of the game is about the qualities of the game.
If it is not about the qualities of the game, then it it is not open to discussion and exploration, except in a post hoc, sophistical way that is not describing what is good about the game.
If it is about the qualities of the game, then we can interrogate that quality and have a critical discussion of the game.
...
Perhaps you are religious? Have you ever thought about the conflict between God being omnipotent and God being omnibenevolent? That discussion in the middle ages spins out of the Euthyphro. Is something pious, the right thing to do because God says it is, or does God respond to rightness and command the right thing?
If the former, there is no questioning or reasoning that opens up God's command, besides perhaps a psychological examination of God. If the latter, there can be discussion of what should be commanded and that is what God would command.
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Bringing this back to games, consider that people (even the same person) do not always respond in the same way to the same things. Does a game blink out of being good with the vicissitudes of a personality? Is there no consistency in quality over what is good and bad if there is no consistency in taste in the person?
Is to be likeable just to be liked? If so, there is no room for critical analysis as to the quality of a game--as to what is a good thing to achieve and what is a good way to achieve it. There is only room for psychological inquiry as a way of trying to predict what someone may or may not like and what may or may not, therefore, be good.
(And the more functional/descriptive analysis you bring up, where certain goals are just handwaved as the target (perhaps the developer's intent, perhaps something a lot of people claim to like), for the purpose of conversation).
...
Perhaps, of course, we are all just geeking out and describing games and trying to find out how it is that they get to us and inexpertly discovering good qualities that aren't really what are doing the goodness work because we want there to be something in the object to hold onto and we want to be able to show the goodness to other people, when really, all that can actually happen is psychological conversion and not responsiveness to things in the game.
EDIT: And perhaps people who do see a difference between how much they like a game and its quality, such as myself, are just into adding sophistical garbage onto a phenomenon that doesn't actually give much room for introspection or critical thought, but...so much the worse for discussion in that case. Unless we just want to swap gaming stories, geek out together, and get pitchforks out together or we want to engage in continual sophistry. I'd rather see it as trying and sort of getting at
something on the best days.
EDIT 2: Perhaps pointed questions help. Do you think people can be unfairly harsh on a game, which does things they otherwise seem to respond well to? Do you think people can have bad taste? If you think either of these things, you do not think simply being liked or not determines the quality of a game.
Moreover, this is not about subjectivity versus objectivity of quality. Sophisticated theories of subjectivity work to mimic objectivity.