Honestly, it's only been adapted twice. Nowhere as much as all the adaptations and homages to stories like The Killing Joke, The Dark Knight Returns, Knightfall, or The Long Halloween. The original story had premise, but it was badly written and the Superboy punch was stupid.
The animated film that adapted the story was much better, and I'm guessing a lot of people's appeal to the story came from that. A cleaner origin for Jason's Red Hood persona, clear writing that actually succeeds in making Jason into a tragic character with understandable motivations instead of an edgy, whiny teen, and terrific voice acting. Jensen Ackles should do more voice acting.
The second adaptation now is this game, and they completely messed it up. They managed to make Batman appear as a neglectful a-hole, while simultaneously make the AK come off as some whiny idiot. I should've sympathized with his plight, but didn't. Too many inconsistencies with his character motivations, and Troy Baker was godawful as AK, particularly once the mask comes off. They should've been honest about AK and his identity, and focus on that character arc instead of wasting time with one of the world's most insultingly predictable "twists".
UTRH remains the greatest argument I've seen for Judd Winnick being a great writer when put under the right editors and forced to trim the fat. Most of his stuff is a little sloppy and light, but he took a decent story in UTH and perfected it to greatness in UTRH.
And yeah, there's some major disappointing elements in AK's portrayal of the character's arc. The idea they had for making him more antagonistic, unstable, and still alive wasn't bad; the idea of the Joker torturing a Robin to the point of insanity and making him a brainwashed Anti-Batman has its merits, and the fakes death removes the need for a Lazarua Pit. But there's far too much of the story afterwards that's not answered. Jason is far too inconsistently portrayed in his demeanor and self control. If they wanted a respected militia leader, then they probably should have had his obsession be more low key and something that is unveiled slowly in the game, and maybe suggest that Jason is fighting his urge to kill Batman.
If they wanted someone as absolutely bonkers as he is, then the game should have had some reason why he didn't just make a bee-line straight for Bruce. Maybe if they'd had Scarecrow discover Jason after Joker's death and set about trying to control him, that would have worked, or have AK and his militia turn on Scarecrow and the rest of the Gotham rogues, embracing the idea that he wants to replace Batman completely and make Gotham safer and used Scarecrow's plan to clear out the innocent so his men could kill all the "scum." Instead, the power dynamics of the villains are all over the place, with the Arkahm gang only seeming to fund and distract Batman when they probably should make up half to three-quarters of the enemies in the game, and it's still very unclear why the hell the militia and its commander work for a guy they effectively recruited.
And again, you can tell the overall story construction was not overseen by anyone who had a Ph.D. In Batmythology; there's too many missed story lines and suggested plotlines that would make the game just a bit better throughout. It's clear that the developers mixed up their Robins, since Tim is effectively the most bland, middle of the road archetype of the name, and they mixed up their Robin and Batgirl romance. Someone should probably be pointing out that Red Hood used to be Joker's handle, since that's the biggest irony about Jason assuming the identity. If Jason is so upset at being replaced, why isn't he attacking Tim or Nightwing, and why aren't those two in the field helping Batman?
Probably the entire Joker's blood subplot could have been dropped and replaced with a few confrontations with AK using Robin and Nightwing. I mean, the idea has some merit, but it's still stupid: the plot point was resolved in AC, the fear toxin is enough to threaten Batman's mind with a Joker takeover so we don't need zombie-Joker blood, and all it does is make Batman do stupid things like lock up innocent people and allies, while also continuing to make Harley a pathetic flunky after they tried to make her better. I appreciate the fun of the subplot, but it wasn't needed, hurt the characterization of Batman, and took the place of other, more engaging possibilities.