No. It's not part of the D&D arm of the old school games. The lineage goes
D&D including Supplement 1: Greyhawk → RuneQuest 1E → Basic Roleplay 1980 → Magic World and Drakar och Demoner 1e → Drakar och Demoner 2e → Drakar och Demoner 3e → Drakar och Demoner 4e aka Dragonbane...
See, the perecentile skills for thieves came from the Greyhawk influence; OE alone lacks anything with percentile skills.
Greg Stafford was blending his Glorantha setting with D&D mechanics. And assigning percentiles to skills other than thievery.¹
Steve Perrin and Ray Tourney took Greg's D&D houserules and warped them into a discrete ruleset: RuneQuest. They removed the d20 and the class and level...
Later, 1979-1980, Greg Stafford and Lynn Willis combined forces to reduce the complexity of RQ into a lighter game, which was released as Basic Roleplay. It was sold as a standalone booklet copyrighted in 1980. It has 4 classes, but they're BROAD strokes, and have some limits on maxima of certain skills.
The following year, a boxed set called Worlds of Wonder was released, including the 1980 BRP and 3 worldbooks. One of which was Magic World. I don't know the direction for certain, but going through and looking at Drakkar och Demoner 1e, the two are super close. There are minor differences, and both were released in 1982.
I don't know the details of DoD 2 and 3 - but Drakar och Demoner 4e is the Swedish and Dragonbane the English title. It's a re-engining of an older setting and tropeset. I do know DoD 3 was still a percentile roll, not a d20 one...
I've heard, but not seen any direct accounts, that Magic World was licensed to help make Magic World...
For reference, DoD 1E, Part 1 is essentially the BRP 1e book. Parts 2 and 3 are the Magic World book.
Most Old School types see BRP as not a direct child of D&D, but I've read that much typed by Greg himself - in discussion of the origins of Pendragon. He just broadened the use...
DoD4/DB is doing the same kind of swap of BRP from 1d100 to 1d20 as Greg did with Pendragon. It's also made a few changes to be less deadly... heal all HP and WP if you get a full night's rest in a safe place. Or 1d once per shift by taking a stretch rest (which doesn't require a safe space). So, if you're not going anywhere, and have no encounters, it's possible to get 4d6 HP back per day... and 4d6 WP, as well.
Comparing this: BRP 1e had a 1 HP per week healing rate... but each wound, each poison, or "fast acting disease" can be treated with first aid - on a success, it's reduced by 1d3 to a minimum of 0. And in Magic World, Spent Power is recovered at 1 point per half hour. That's actually a little faster than in DoD4/DB.
DoD 1e has the same 1 HP ("SP" in Svensk) and MP ("KRA") per half hour.
¹: Greg wasn't the only one to latch on to the percentiles from Sup 1 and broaden them a lot... Kevin Siembieda, Frank Chadwick, and a number of others from that generation did so. Siembieda's Palladium of Desires campaign was doing 3d6 stats, 1d20 combat, and 1d100 ≤ skill for non-combat. Chadwick's 1983 1st edition Twilight 2000 was a 3d6 stats, roll 1d100 ≤ skill, game, too.
