I don't think they do much investigative journalism, but I've found Rock Paper Shotgun to have some more thoughtful pieces among their more traditional reporting.

Uppercut, Unwinnable, and Into the Spine sound to me like what you're looking for. Paste has quietly raised up a lot of great games writers, too.

I also recommend reading lots of reviews for games you're interested in. Listen to spoilercasts about them. Pay attention to the bylines, and when a critic says something that gets your mind going, try checking out what else they've written. Most critics are active on social somewhere, and if you like what they have to say, they'll probably share other writing that's similar.

I'll be keeping an eye on this thread because I would also love to know if I'm missing out on some good games journalism out there. Sadly, sites like what you've described are increasingly rare in the modern era. Nevertheless, here are a few that come to mind:

NintendoLife is pretty great for this if you're looking for Nintendo-related news, reviews, interviews, and feature articles.

One of their affiliate sites, Time Extension, is also really good for long-form articles and retrospectives about retro games.

And while it's mostly just news, like you said, Polygon will sometimes surprise you with some really excellent feature articles that have a lot of thought and research put into them.