Not at all... the dimensions of string theory (ST) are ten (or so) space dimensions. The video you point to departs from possible analogies with String Theory when it starts looking at time as the fourth dimension (the analogy is fine up to then, but it would need to make the point that, although time is useful for the explanation, in ST the new dimensions are not extensions of "time").
Then, its depiction of the higher dimensions as all possible histories and all possible universes is an interesting fabrication, but has nothing to do with the ST description of the way nature may work.
Either way, my point is that the video linked makes it look as if dimensions 4, 5, etc. have to do with time, histories, universes, and such, while ST refers to space-like dimensions (along which, as in regular special relativity, one can have Lorentz boosts that "mix" them with time,... but this is not the central point).