4e has no "massive damage" rule.
The rule you referenced is only applied when making a Coup de Grace attack, which requires the target to be helpless. Unlike many other editions of D&D, the 4th edition has no rules that would cause a creature in standard combat (as opposed to special circumstances, such as being helpless) to risk instant death from an attack that deals a large amount of damage but does not reduce the creature to zero hit points.
A group could, of course, introduce such a house rule for this purpose if they so wanted; nobody is going to kick down your door and arrest you for modifying the rules. However, it's important to remember that the rules were written by professionals who would have included such a rule if they thought it would improve most groups' play experience. Much like an automobile engine, tinkering with RPG rules is likely to end in problems if you don't know what you're doing. Off the top of my head, I can think of several ways adding such a rule would influence the game, some of them beneficial and some of them not. In particular, it's worth noting that later 4e publications (generally from MM3 onwards) opted to give foes higher damage and less health, to speed up combat; this increases the likelihood that rule will trigger for both sides compared to what you might be expecting from looking at earlier books.
What are "hit points" anyway?
There are two aspects to most roleplaying games: rules ("crunch") and fiction ("fluff"). When Bob describes his character, Grognar the barbarian, swinging an axe at a nimble pixie, that's in the fiction. That description is then translated down into the rules as an attack, which is resolved, and the result is then translated back up into the fiction. So what does it mean in the fiction that a 7' tall half-orc "hit" a 1' tall pixie with a huge axe and did 16 damage out of its total 58 HP?
From the PHB, p293 (emphasis mine):
Over the course of a battle, you take damage from attacks. Hit points (hp) measure your ability to stand up to punishment, turn deadly strikes into glancing blows, and stay on your feet throughout a battle. Hit points represent more than physical endurance. They represent your character’s skill, luck, and resolve—all the factors that combine to help you stay alive in a combat situation.
This is hugely important. When an attack deals hit point damage, that does not automatically mean it dealt physical damage to the target; it reduced the target's ability to stay in the fight.
For a creature like a troll, which relies on being big and tough and regenerating, that damage may very well be represented in the fiction by actual physical wounds. On the other hand, a high-level rogue could have several times as many hit points as that troll, but would die from even 10% of the physical wounds it would take to incapacitate the troll. Her hit points are instead more likely to represent the ability to throw herself out of the way of attacks. An attack that deals no damage to her is one that's easy to avoid, while one that deals hit point damage is effectively forcing her to really exert herself to dodge it. Eventually, she'll run out of the stamina/endurance needed to keep making those incredible dodges and a blow will reduce her to 0 HP, which would translate into the fiction of actually finally physically hitting her. And like most humans, one good, solid blow with a sword is enough to incapacitate her.
This separation between "hit point damage" and "physical damage" is why non-magical means like taking a short rest or being shouted at (encouragingly) by a warlord can restore hit points, even though they couldn't do much about physical wounds.
What, then, would a house rule that causes a target struck for a large amount of HP damage to risk instant death represent in the fiction?