The NYTimes is widely known, read, and linked to across the web, so it's not surprising that it shows up on HN as well with regularity. There's nothing going on with respect to voting rings or whatnot: I'd be surprised if there weren't more than a few NYT (or WSJ or WaPo) submissions on the front page every day just due to their prominence as publishers.

While I'm sure there are HN members who have subscriptions, as you note, there are a few articles available for free, and there are a few workarounds for the paywall as well, often posted in the comments.