Director John Singleton basically came up with the whole thing (including the Ancient Egypt concept).
Michael Jackson also contributed by wanting, for instance, the American basketball player Magic Johnson to appear on it.
In any case, the 'Remember The Time' music video should not have included the Ancient Egypt concept because that concept does not fit some of the song's lyrics.
For example, Michael Jackson at one point sings "you and me, in Spain", but Spain did not exist yet in the Ancient Egypt period.
Or, at another point, Michael Jackson sings "on the phone, you and me", but phones were not invented yet in the Ancient Egypt period.