After watching the video featuring the Mysterious Figure's moveset, I can't help but wonder whether this power is what Master Xehanort ultimately wished to acquire. With Terra's stronger body, and the X-Blade's power at his command, Xehanort would have been able to survive the Keyblade War and gain control of the light that supposedly has influence over all things--possibly creation itself.
If the Mysterious Figure was able to acquire that power (at any point in time, even the distant future), it would account for not only all of the techniques borrowed from other characters, but also his apparent abilities of time travel, since someone with power of that magnitude (particularly power of creation and preservation) would naturally have all of time accessible before him at once.
Granted, this is only an incredibly vague shot in the dark, inspired by the X-Blade-style attack he executes. Honestly, though, I'd just prefer the Mysterious Figure to be solely a gameplay-centric experience, since any story that integrates time travel into its plot is almost certainly bound to degenerate in quality.