Yeah, that's an over-run. It's happened a lot.
Rough on the plane and company, and possibly the pilot's
career. Absolutely nothing to be sad about, at all, with this one. The over-run area did its job in getting the plane shut down well. Grass is a tough mistress if you're trying to land on it, but it's wonderfully gentle when you need it to stop your plane. There's been jets who've taken a dive into the trees at the end of the runway.
Losing a nosewheel is always tricky, because in some cases, you're better off landing
completely gear up, and other cases you're better off landing on the mains and holding the nose off until the plane completely stalls out. Never had it happen to me, but an instructor had to "slap down" the nose gear on a small prop. You come in fast and literally bounce a couple times in an attempt to get the nose gear down and locked. Aside from
complete hydraulic loss, "slapping down the nose gear" has always been a prevalent scenario in my aviation nightmares.
Although, there was this one time, had I bounced for the third (and final, let me tell you) time, I would have had that sob slapped down
real good...