Well *I* usually say something like...I've been thinking of an approach like that, at the very least as a framework for organizing presentation in a tutorial rulebook, but also as a way of running an introductory game.
"Can you give me 10 minutes?"
By that time I'll have 'em so deep into an adventure (no detailed PC to start -- just "you're a Fighter, fully equipped, okay? -- winging it all the way) that they can hardly believe it. "It's THIS easy? Whoa!"
- Start with no rules, just a character and a situation.
At this point, all you the GM are interested in is whether what the character does sounds like it would reasonably work or not. If the player asks questions, make up appropriate details. Always make sure you either ask "What do you do?/What do you want to know?" or that what you say implies those questions as a follow-up.
- Don't say "no" to actions, just make options interesting.
GM: "There's a rope bridge about a half-hour away, but you'll have to cross through the dark woods to reach it, unless you want to backtrack for a couple hours."
Don't try to prevent the player from avoiding the bridge, just make sure every option you present has a chance for things to happen.
- Add attributes first, as just a way to judge capabilities.
GM: "It's pretty big and requires someone a little stronger than average, just to be able to shift it. Let's roll some dice to rate your relative Strength from 3 to 18, and if your Strength is 13 or more, you can move the tree."
For a beginning scenario, you probably won't need any attribute other than Strength, Dexterity, and Intelligence. Introduce them as necessary.
- Introduce potential bad stuff as random 1 in 6 chance in risky situations.
GM: "The tree is so close to the moat, there's a chance you might slip and fall. I'll roll a d6 and if it's a 6, you fall."
Don't have the fall do damage at this point; introduce one mechanic at a time.
- Introduce ability checks.
Player: "I'll swim to the far bank and climb out."
GM: "To fight the current, you have to roll these dice and beat this number, based on your Strength. Otherwise, you'll be swept to the same side of the river you started on, but you can climb out there."
What "these dice" and "this number" are depends on how you handle these checks. The simple route is either a d20 or 3d6 <= Strength. I would instead say "You normally need to roll a 3 or less on a d6," and if Strength is less than 9 or higher than 11, I'd add, "but because you are weak (strong,) the number is..."
- Introduce a contest of Strength (Dexterity, etc.)
Player: "I try to pull him out."
GM: "He's so panicked and thrashing around you actually have to struggle against him. He's kind of a weakling, though; his Strength is 5. You need to roll the same number as when you fought the current, but this time, you get a bonus because your Strength is higher than his."
Just set the Strength (or other attribute, in other situations) lower than the player's character, so that the player sees that stronger than an opponent = better chance.
- Introduce damage and hit points
Tell the player that there are 3 boulders, so the saving throw is reduced by 3 points. If the player fails this save, say something like "Normally, a hit like this would kill a normal man, but if you have luck, you might be able to survive a couple potentially deadly hits. Let's roll a d6 to see how much luck you have." The boulders do only 1 point of damage, no matter how many hit points the character has.
- Throw in a fight
The bandit has 2 hit points and the equivalent of leather armor; he's a 0-level man, while the player should be treated as a 1st-level fighter. Roll a d6 for weapon damage. Let the player try any tricks they want; it doesn't matter if the player kills the bandit or not, but whether there's a standard combat roll or two, to show how combat works.
- When someone is injured, show how to save people
This can happen no matter who is injured, although if you play with 0 hp = instant death, you might want to have the monk take pity on the bruised character instead. If magic is the only healing you allow, have the monk pray and cast Cure Light Wounds. If you allow first aid, use whatever mechanics you prefer; I allow restoring 1 point of damage on an appropriate attribute check for all kinds of things: bandaging, a good meal or drink when hungry/thirsty, pleasing music from a bard, etc.
- Keep playing, improvise based on the above rules