I think these days I'm mostly nostalgic aesthetically more than substantively. For example, the pixelated characters and ToeJam & Earl-inspired music definitely like Diaries of a Spaceport Janitor more appealing to me as a somewhat older gamer who grew up back when that was standard-issue stuff. But thematically, Diaries is also a pretty unique game, focusing on conveying the challenges of just living life as a working class person and wanting to escape into adventures (read: metafiction for video games), but being unable to afford to because you live from payment to payment. I like how it uses retro aesthetics while substantively embracing a very distinctive identity and heartfelt message.
Same thing with my favorite game of all time: Gone Home. It's set in 1995 and includes all kinds of nostalgic references to that era: VHS tapes, audiocassettes, bubble-screen TVs, the Super NES, and the classic arcade hit Street Fighter II from that era. I wasn't much younger than the game's protagonists in 1995 either possessed a somewhat similar personality to what we learn about Lonnie's. In all these ways, I can relate to it on a personal level. Substantively though, Gone Home is NOT a traditional type of video game, but something very bold, progressive, and unique, both thematically and in terms of how it's played.
See THAT is the essence of old-school gaming, in my view: for developers to make video games from the heart rather than on tailoring everything to the tastes of focus groups and what venture capitalists are willing to invest in. Smaller developers who can't get venture capitalists to fund them and may be unable to bring in focus groups and such still tend to rely on that older process of product evaluation: if they (the developer) likes it, somebody else probably will to. That kind of approach. THAT, sincerity, is the ultimate form of callback to the older times and, as such, the ultimate way of appealing to me. That's the key ingredient that older games usually had that modern games usually lack and the thing I miss the most about them.