What I consider good design

So, one thing that I've been considering recently is what a 'well designed game' even means to me.

I don't think "Is it fun" covers it. Basically any game can be fun if you play it with your friends and the chemistry works. I've had fun playing Pathfinder, because I was playing with my buddies and we were bouncing off each other, but that wasn't because of the game's design. We'd have had just as much of the same amount of fun with any other game, really.
And, conversely, plenty of really valuable experiences I've had with RPGs have hit me with darker emotions. Pain, grief, regret, fear... these can all produce intense emotions that make a game worth playing in my view.

So, what am I looking for?

After some thought, I figure I want a game to
create a specific emotional experience when I play it
and the better it does that, the more successfully it does that, the better I consider the design.
The specific emotional experience will obviously vary by game. OSR games create nervous tension like a survival horror game, Monsterhearts produces messy bitchy angst, Duneon Bitches gives you defiantly vulnerable hope. But I look at the experience the game tries to create, and if it does that, it's well designed.

But lets go into a bit more detail. How do games achieve this? How do we judge what they're doing?
Three ways come to mind:

1: Set expectations
2: Shape play 
3: Cover creative gaps

The better a game does these three things, the better it will create an experience, and the higher I rate it.
Let's go into each of these in a bit more detail.

Setting Expectations

This bit is all about communication. I open the book up, browse its fluff and mechanics and look at the art and graphic design, and I get inspired. It makes me picture what it's about, the feelings it wants to evoke, the themes it wants to explore.
This isn't just about the mechanics specifically. There's a reason so many RPG books start with a couple of pages of fiction to set the tone (or with several dozen, if they were made by white wolf). Same goes for visuals; The Stygian Library would feel totally different without Alec's art and Anxy's layout. It all serves to put you in a particular headspace when you go through the book.

A game doing this bit well has everybody come to the game already imagining what the game could be like. That image in their head will be strong, and will be similar. Everybody goes in on the same page.

Shaping Play

This is what most people think of when they talk about 'game design'. Things like how characters are designed, how events are resolved, and so on.
And this shit absolutely matters. Sure you can freeform things, or make every resolution mechanic up on the fly as you go, but that won't create the same experience. Game mechanics push and tug you in particular directions, the limit you in some ways and open up possibilities in others. 
Think of it this way: compare a fight in D&D 5e, and one in Dungeon Bitches. Even if you go in with the same starting fiction (the same location, characters, enemies, etc), the experience will be totally different, because the mechanics care about different things. In D&D, the fight is resolved round-by-round, its a chance to use various character tools, the consequences are (relatively trivial) physical injury and depletion of material resources, everybody gets to contribute about as much, and the PCs are pretty sure to win. The end result is empowering, tactically challenging - fights in 5e feel good. Compare to Dungeon Bitches. The fight is resolved with a single roll, only one PC's capabilities directly shape the results, the consequences might be emotional trauma or gruesome injury (both of them very hard to mitigate), and there is never a clean win. In DB, violence feels nasty and frightening, and characters respond to it far more seriously. 
This is a small example, but it applies to broad structures too. Who even are PCs? What capabilities of theirs matter? What tools do they use to influence the narrative? What rewards and disincentives shape their actions? All of these things will create a particular experience in play.
Like, here's a really simple example. The tension you get making a jenga-pull when you play Dread creates a feeling of mounting nervous anticipation that you wouldn't get if the game wasn't using Jenga as it's main mechanic.
This isn't just mechanics, either. The fiction matters. A setting without law enforcement plays very different to one with incredibly strict law enforcement, for example. That stuff shapes play, too. You'll have an easier time telling stories where PCs struggle with predatory instincts if - in the fiction - all your PCs are vampires.

Covering Creative Gaps

Its nice to imagine that we can simply draw on our infinite imaginations to create all the details and ideas we need for a good experience at the table, but that's just not true. There's going to be moments where nothing immediately comes to mind, or you would normally tend towards the generic. So, here, the game provides concrete examples, so when you might hesitate creatively, there's inspiration to fill that gap.
This might be the way a lot of PbtA moves offer specific options to pick between when they resolve. This might be the use of random tables (such as wandering monsters) in play. This might be pre-packaged character archetypes that clearly communicate the sorts of PCs you might play.
This is something a lot of design neglects. Vampire the Masquerade, for example, doesn't really provide much in the way of concrete examples to draw on. Want to run a feeding scene? The vessel, and how they're approached, has to come from the ST - there's no 'big list of vessels' you can pick one from for a side-scene where a PC feeds.

So that covers it, I think. I want the game to clearly communicate what it's about, for the procedures of play to nudge and push the game towards that experience, and for the game to pick up the slack where the participants might falter. If a game does all of these things, I can be pretty sure that I'll come away from it having had the emotional experience I was looking for. And that's a success.