From what I saw it's part of the company culture. Managers were there late so of course their subordinates didn't want to leave and be seen as not working as hard.

Also there's no concept of overtime with salaried fulltime employees. You might work 100 hours in a week and you're still taking home the same paycheck as if you worked 40 hours. That's just the way corporate America works.

So they can get a free dinner? Or maybe they're just happy to work a bit late, avoid peak-hour traffic, and then head home?

I work 6am-10pm one day a week voluntarily, though I work for myself. I avoid traffic, parking is easier, and I get the office to myself without distractions for about 6 hours.

They're working late so that they'll still be at the office when the free food comes. That's the point of the late free food.