"The Xth Law of the Yama:
As long as one is victorious in one hundred games, one will be able to return to the state one was in 0.01 seconds before death and survive!" (Pg. 2 of Ch. 11)
In other words, even though in this dimension they have already died, if they fulfill these requirements they'll go back in time just a tiny bit and be saved instead - so in the MC's case, all those people trying to find him will get to him in time to resuscitate him.
Also, see shojoshit's post below; I think they explain the concept of the whole story pretty well. (⌒▽⌒)
I don't get it. How is 0.1s before your death gonna help you? Won't you still die?