It looked like everyone was playing man coverage, except Haden and Davis who were playing zone. Probably because they were directly behind the CB who lined up against Hogan, who blitzed instead of covering him.
Burnett is pretty clearly shadowing Gronkowski's movements in man coverage, but since the tight end stayed back to block, that meant Burnett was just sort of standing around near the line of scrimmage. Williams - who would've been the underneath help on that side of the field - was shadowing Edelman, who came around for a fake reverse. Of course, there's another whole line of debate about whether having your slow ILB covering a wide receiver (either Edelman or being the underneath help on Hogan) is the smartest idea in the world, but in this case it didn't matter.
So basically, the two guys playing zone coverage were both on the left side of the field, and there was only one safety deep because Burnett was manning up on the tight end - so on a left-to-right crossing pattern, if Davis doesn't pick up the receiver coming across, you're dead. If anything, Davis was the one who botched that. But it probably would've been a good 20-yard completion anyway, because unless Davis anticipates the play and reacts perfectly, there is an unavoidable window where the receiver is going to be open.
The big problem is that we had three guys standing around with no one to cover because of unfortunate formation matchups (Haden, Burnett, Williams) and the one guy who could've most likely prevented the big play (Sutton) was rushing instead. A bad time for a biltz, an imbalanced scheme because of that, and a missed read by the safety who was the last line of defense, even though that would've been a difficult play under any circumstances. Basically everything went wrong.
Side note: This is exactly the kind of defensive alignment that you could take advantage of if you were, for example, a coach watching the pre-snap movements from upstairs and communicating to the quarterback all the way up to the snap. If you had a second radio in the quarterback's helmet, and the tendency to employ it early in the game to try to establish a lead, and late in the game to pull off "miraculous" comebacks, it would fit right in with that pattern. But I don't know of any team that does that. Do you?