I remember, when talking about this game on the Red Thread forums, how the game always reminds me of Stein's Gate -- Not solely due to how it paces itself, going from down-to-the-earth scenario to tense psychological thriller but also how it frames its concept of time travel.
It's seem go to about it within the lines of the Grandfather paradox; or restricted action resolution, something quite similar to that of A Roswell That Ends Well episode of Futurama. If one were to travel back in time, then the laws of nature would actively make it impossible for the traveller to do anything that could prevent their time traveling from not actually happening. Examples like the traveller's grandfather surviving fatal occurrences, stumbling, falling down tall heights or physical assaults, said grandfather is injured but not killed, it is not in fact possible for him to die, unless he was supposed to! If said person were to be killed then it'd usually turn out that he wasn't the traveller s actual grandfather. No action the traveller makes to affect or change history can ever succeed, as some form of "bad luck" or coincidence always prevents the outcome.
More often than not, the time traveller does not merely fail to prevent the actions, but in fact precipitates them, usually by accident as well. I also like to think it's the case of multi-verse theory here as well, due how similar it is to that of Stein's Gate, like say when Maxine travels far enough she actually enters a different timeline altogether, 'uploading' her mindset to that new world's Maxine, but the latter also involved a case of "self-healing" timelines in its narrative which might be the case here too. It's supported a bit in regards to the whole ordeal of preventing William from dying, said casualty must be constant: i.e. nothing can occur in the absence of cause -- In other words, preventing a cause from 'effecting' might still have it remain a constant even if it was "eliminated". Like hurling a rock into a pond, it creates ripples, they spread but are ultimately consumed by the waves that sprouted from it.
Were someone to say, go back in time and assassinate Hitler, whom waged an awful war on most of the world, preventing him from doing so, could ultimately result in his followers using said assassination as a subterfuge for war, ultimately using the emotional effect/impact to filling out the hole. Preventing a loved one from getting run over by a car, only for said loved one to be killed by a mugger (Steins Gate, The Time Traveller from 2002).