Everytime you die, you come back at the beginning of the four days sequence, but with new pieces of information (eg : after your first death you learn that someone wants to kill you, and that Polonius sleeps with the Queen).
You can deliver ALL piece of information to ALL characters, but it is a really, really bad idea. if for instance you tell everyone you live in a time-loop you will be brought to a convent because you are crazy. Tell Hamlet that the man in the Queen's room is really Polonius, and now he wants to kill both the Queen and the King (and Polonius).
The whole point of the game is to deliver the correct information to the correct person to change the sequence of events, learn new information, die again, and give that new information to another person until you break the curse. You have a lot of way to throw spanners at the play (eg give an information, but also stop someone from meeting someone else at a critical moment, etc) but fate [and maybe a little someone] has a way to bring any change to an equally as bad, or worse outcome, so next life you are trying to either try to prevent the future bad / worse outcome, or maybe try to modify the sequence of events if a different way.
There is a limited inventory ; you don't have an inventory menu but you can for instance get the key for the room of the Queen consistently (every life) once you know where to look, which of course is an information you can get by helping some characters in some timeline.
The game starts slowly (first "life" follows the events of the play, so if you know it either you can play your Ophelia role, or you can watch what happens on the side, for instance follow Rosencrantz and Guildenstern for two full days to see what they are up to, and possibly learn a few things along the way). After your first death, the game really really opens and I really felt like I was free to change the course of events with just one word at the correct moment.
Groundhog day : the game !