Objection! The Phoenix Wright games are not such a great Rationalism-didactic game!
My wife's a big fan of the series. While they're pretty good games and have funny dialogues, I don't think they're great tests of reasoing and cleverness. They're a bit better than the old point-and-click games (where you often had to fall back to "try everything with everything"), but not by much.
A lot of the things you mention are only present in the story, so they don't matter nearly as much when it comes to teaching things to the player. And plenty of games have stories that feature the elements you mention - life-and-death situations, the end justifies the means, you have to try everything, etc.
And one aspect of the game seemed anti-rational to me: that your client is always innocent; i.e. you always know the bottom line, you just have to find arguments for it. One way people shoot themselves in the foot is by taking a certain position (a split-second judgement on superficial features, or based on their peer's positions, or political affiliation, or fashion ...), and then filter evidence depending on whether it fits your conclusion or not, only changing their mind if clobbered with opposing evidence.
In terms of teaching how to think, I'd value complex simulation games above the Phoenix Wright series, or competitive multiplayer games - the best would probably be things like diplomacy, where you have to make alliances and may or may not hold your word. I know there are some webbased or play-by-email games, but haven't played any like that for some time now.
Hold it!
There is little to no Gameplay And Story Segregation: the quest for truth by disentangling lies with evidence being the key difference with any other game. (Except perhaps L.A. Noire but I haven't played that one yet so I can't say.) Other adventure games usually rely on your solving a gratuitous amount of puzzles: it's basically an expanded Rubik's cube. Do Rubik's cubes teach you the rationalist virtues of seeking the truth for its own sake and abandoning lies with haste? I think not, and neither does any other game as far as I know.
Also, for on...
This article aims to prove that Ace Attorney is possibly the first rationalist game in the lesswrongian sense, or at least a remarkable proto-example, and that it subliminally works to raise the sanity waterline in the general population, and might provide a template on which to base future works that aim to achieve a similar effect.
The Ace Attorney series of games for the Nintendo DS console puts you in the shoes of Phoenix Wright, an attorney who, in the vein of Perry Mason, takes on difficult cases to defend his clients from a judicial system that is heavily inspired by that of Japan, in which the odds are so stacked against the defense it's practically a Kangaroo Court where your clients are guilty until proven innocent.
For those unfamiliar with the game, and those who want to explore the "social criticism" aspect of the game, I wholeheartedly recommend this most excellent article from The Escapist. Now that that's out of the way, we can move on to what makes this relevant for Less Wrong. What makes this game uniquely interesting from a Rationalist POV is that the entire game mechanics are based on
That the judicial system is Japanese-inspired also means the legal system is inquisitorial: the court has an active role in the case (whereas the adversarial system in the West reduces the role of the court to a form of referee) and its (alleged) mission is to dig out the truth. That and the lack of in dubio pro reo mean you can't just be content with putting your client's guilt in reasonable doubt, you have to thoroughly prove their innocence and find the true culprit and get them imprisoned. That means you have to find out the entire story and you can't leave any threads hanging.
Additionally, the fact that you are a lame attorney facing an unsympathetic judge and egomaniacal, dirty-playing, high-status prosecutors who *have led the police investigation and only prosecute when they think they have all the cards in their hand* means you will. not. catch. a break. Every single move you make will be scrutinized, you will face constant sarcasm, dismissal, condescending and ridicule, and sometimes a single mistake on your part (presenting the wrong piece of evidence) can cost you the entire case. This game forces you to take an unflinching stand for the truth in the face of every social sanction imaginable (including, obviously, attempts at your own life). Of course, the plot goes out of its way to make things difficult for you: everyone is as unhelpful as possible, and even your clients need to have the truth pried out of their mouths with the determination of a dentist. Other witnesses can cast remarkably subtle webs of lies that really force you to think out of the box in order to find their weak point. And, since the cases are Always Murder, your client's life is always on the line, and that's when you don't have another person in grave distress. This serves to motivate you and draw you into the story, but it also adds to the constant pressure you are in to find the truth.
But that's not all. In the latest sequel, Ace Attorney Investigation, you take the role of Miles Edgeworth, a prosecutor who Defected From Decadence and restricts himself to ethical methods in crime-solving, eschewing the questionable methods he used in the past, and which most of his colleagues still practice with abandon. The battle doesn't take place in court (which, unless Phoenix or his successor Apollo are defending, is but a formality) but during investigation, which is where the case is won for a prosecutor (if they aren't certain they have enough evidence to get a conviction, prosecutors just don't... er... prosecute). This means you have to investigate the crime scenes, interrogate the suspects, and find the connections between the clues in order to reconstruct what happened. This is represented in the game by an entire gameplay mechanic for logical deductions (and a fair bit of Will Mass Guessing) that are hilariously over-the-top, concluding with a literal "Eureka!". The interrogations are no piece of cake either: oftentimes, (and, surprisingly, realistically enough in a police investigation) you have to take your suspects through excruciating logical baby steps to break their lies, since they can rely on something as cheap as semantics. Actual Eureka Moments, that is, sudden piecing of mental puzzles in a moment where deductive thinking is stalled, thanks to someone saying something unrelated that just happens to trigger the right association, is also a common phenomenon during investigation: composing a good hypothesis with nowhere near enough evidence is, of course, another rationalist skill, one that is underrated by modern Science as it is now.2
So, to sum it up, what virtues does these games teach?
I rest my case.
1. Sorry, couldn't resist the reference: I'm just that geeky. Sue me.
2. That, and, honestly, who could resist a game that names one of it's tracks "Logic, The Way To The Truth" and, when winning a case, "Solution! Splendid deduction." "Cornered", which plays when you are punching a hole in a witness's declaration that is so huge it could swallow galaxies, leaving them no room whatsoever to continue with their lies and often leading to spectacular villainous breakdowns(MASSIVE SPOILER ALERT), remains an all-time classic. (One clip is even peppered with quite interesting quotes on Truth.)