First, that D&D demo is one of the scariest things I've seen in a long, long time.
Second, a D&D Lite outline possibility:
Core Rules (defining): [est. 4 pages]
- Task Resolution: Describe checks and DCs, as well as opposed checks
- Characters: Ability scores (reduce these to bonuses and penalties, base range of -3 to +4) race, and class
-- In gameplay: Describe hit points, armor class (perhaps call it Armor DC?), mention class abilities.
-- Experience: Leveling up, et cetera. Goes to level 10. Bonus abilities at 3, 6, and 9.
- Combat: Describe initiative. Reduce to one action, either move, attack, et cetera.
-- Attacks (attack check versus armor DC)
-- Spells (spell check versus save DC)
- Saving throws: Class-dependent. Only one base save DC (increases per level), to which requisite abilities are added.
- Skills: Skill checks use the most closely related ability modifier. Certain skills have an extra bonus dependent on class (equal to +1/level of that class.)
- Feats: One at first level, fourth level, seventh level, and tenth level.
Races: [Est. One page]
- Humans (No ability changes; Bonus feat at start.)
- Dwarves (+1 Con, -1 Cha. +2 save DC.)
- Elves (+1 Dex, -1 Con. +1 to spell checks.)
- Halflings (+1 Dex, -1 Str. +1 to armor DC and attack check for size)
Classes: [Est. Four pages]
- Fighter
-- 6 + Con hit points per level.
-- No skills
-- +1 attack bonus per level
-- Middle save progression
-- Special: Bonus fighter feat at even levels
- Cleric
-- 5 + Con hit points per level
-- Skills: Knowledge (Religion)
-- +3/4 attack bonus
-- Slow save progression
-- Special: Spells (mainly healing, turn undead, etc)
- Rogue
-- 4 + Con hit points per level
-- Skills: Bluff, Disable Device, Open Lock, Search
-- +3/4 attack bonus
-- Fast save progression
-- Special: Sneak attack (+1/level, simplified rules)
- Wizard
-- 3 + Con hit points per level
-- Skills: Spellcraft
-- +1/2 attack bonus
-- Middle save progression
-- Special: Spells (simplified to mainly attack spells)
That can be covered in less than 10 pages. Then all you need is tables for the classes (progressions, et cetera), and a brief spell list, and you're set. Could easily be done in under 20 pages (although it would need a decent DM to run it without extra supplements... it adapts pretty readily to standard D&D, with the only big change being the reversal of check & DC with regard to spellcasting.)
(Edit: The outline has been errata'd so that Elves don't get a penalty to Cha

)