I don't entirely agree with either of you.
It all depends on the context.
A lot of the time online when someone says "This game is good", its because they enjoyed it, not because it is objectively good.
However, when they say "Its a good game, but I didn't enjoy it", it can be that they enjoyed certain aspects of the game, but not it overall, or they may have enjoyed nothing but seen potential for a different audience to enjoy it.
Even then sometimes people will state good games based off semi-objective qualities to try and escape subjectivity, even though that is impossible. The main thing here is what constitutes good, what constitutes bad, and what constitutes mediocre, though all these things will change from conversation to conversation.
A number of people think that a game is only good if they enjoyed it. This works for them, but is utterly useless for defining whether a game is actually good or not, and something someone should think about buying. I enjoyed the first half or so of Duke Nukem Forever, though many people hated all of it and consider it a bad game.
Other people think whether a game is good or not should come down to its more objective factors - Aesthetic, Smoothness of play, Story - however whether each of these is good is also subjective, and based largely on the above problem that it is enjoyable, but that changes from person to person.
In general for a good game, I look for nothing more than polish. It may be enjoyable, it may not be, but if it is very well polished I will feel like I got my money's worth out of it. In general, if its polished, it will have a good aesthetic, smoothness of play and story, though people prefer different things along those lines I try to cut that out and work by the style the game seems to be aiming for, and how it executes that.
This has flaws in that, whilst less than the simple "Its enjoyable" definition, it is still effected by subjectivity, and it still doesn't tell you whether a game will be enjoyable or not.
Overall, deciding what constitutes a good game from an objective point of view is impossible, and doing it from a subjective point of view is pointless. This is why I rarely watch/read reviews. Instead, I read the objective facts about the game - what its controls are, Look at pictures of what its graphics and aesthetic look like, read up on any bugs, its system requirements to determine its Framerate on my machine, and then gameplay on Youtube to see how it works [Or playing a demo in store or at a friends]. That is far more valuable information than whether someone enjoyed a game, and allows you to decide whether you are likely to enjoy it, which the statement of "This is a good game" can not do.
Why? Because an objectively good game does not exist, and whether one person subjectively enjoyed a game has no bearing on whether you will.
