The reason it won't run is pretty much the same reason why rendering low-end games WITH your processor never really ends up in anything looking good or running smoothly.
Chipsets are like, cheap processors that can display things on a monitor.
My sister can run Sims 3 well on integrated graphics, it's hardly a what I would call a game, but it requires decent 3d performance nonetheless. The requirements for DayZ don't look demanding at all, it would probably start and run, performance wouldn't be great but I don't see why it wouldn't be playable.
But if OP's computer is broken it couldn't hurt for him to get a new one.