For games, the closest is indeed Deadly Premonition rather than just bits that remind of TP, though I'd say Deadly Premonition becomes its own beast even if it is wearing its inspiration on its sleeves.
I've watched several Twin Peaks inspired by shows, and I think the closest and my personal two favorites that hardly get mentioned:
-Happy Town, this was a one season show inspired by TP, it isn't just like TP but I think the influence shows stronger in this one than many. I think something that helps the show a lot is a number of the characters are quirky but entertaining in an overtly dramatic way at times as we see several characters plotlines advance during the season, and there's a subtle surreal element that's actually very interesting that begins to creep up more and more as the season goes on, but ultimately will remain unanswered because while the show had a pretty good cliffhanger it's never going to be continued now. It's one of my favorites of the rip-offs, it's not just like TP but I think it managed to capture more of what made the original series good than most. It's only about eight episodes and I'd recommend it (though fun fact, this show did so bad in viewership that they just released the last two episodes online to download).
-Bright Falls, this was a mini web series that was made to promote Alan Wake before it released starring a different character living in the game's fictional town of Bright Falls. It was six episodes that were around 5 minutes each, so the whole thing is only about 30 minutes. It manages to be a lot better than I think one would think it'd be, hell I'd even say while not really a movie it's the best 'video game movie' ever made (in fact, I think I might make a topic about this). It's a bit darker than the original series, but it manages to get surprisingly close to some Lynchian tones (though it's not quite as mysterious because it's a prequel to Alan Wake, and if you know what AW is about you pretty much know what's going on, which I think both adds and takes away from it in ways, but is completely worth watching).
What I think.