Magoi Manipulation simply means manipulating the rukh in your body and turning it into energy (magoi) with your body – similar to ki, nen, etc. By doing so, they can use magic. Side effects of using too much magoi include exhaustion, bleeding nerve endings, shortening lifespan, and death.
All magicians are naturally born with the ability to manipulate magoi, which allows them to use the different types of magic. They don't have to "learn" how to manipulate magoi since they do it unconsciously.
Magi are loved by the rukh, so they can use unlimited magoi and can manipulate it better than anyone else.
While only Sinbad, Alibaba and Hakuryuu have shown to use the specific magoi manipulation you guys are talking about, it actually doesn't amount to much. Sinbad and Alibaba had to learn it because they had irregularities in their rukh that hindered their ability to use magoi like other humans (Sinbad had white and black rukh from a curse, and Alibaba had his and Cassim rukh which was tearing his body apart), thereby preventing them from Djinn Equipping properly. Hakuryuu on the other hand needed magoi manipulation because he had no metal vessel, and thus relied on a magoi imbued weapon like the Yambala Tribe.
No one else had to "learn" magoi manipulation like Sinbad, Alibaba and Hakuryuu did because they had no reason too -- no one else had irregular rukh or were as weak as Hakuryuu. Everyone who has a metal vessel, household vessel, or magic item has to, by virtue of the weapon, learn to manipulate their magoi to use the magic through household vessels and/or djinn equips (like Sinbad taught Alibaba during the Balbadd arc). That's why none of the generals had to use the same skills Sinbad did, considering they only have white rukh and use it with their household vessels to use their magic skills (and Yamu as a magician had no need to learn it because she's a magician). Likewise, Mor was freely manipulating her magoi in Zagan's tower against the mobs through her household vessel, which led her to becoming sick from magoi depletion.
It seems you're taking this literally, "magoi manipulation" is a skill only a few are shown to have like the Yambala nomads, Sinbad, Hakuryuu and Alibaba. What you're talking about is the ability to use and control magoi which although this might seem counterintuitive is not the same thing as magoi manipulation.