I can find competing evidence that it's not dimensional. I know the Lyxen has done that already.By the way, I just find this in the DMG.
"DIMENSIONAL SHACKLES
Wondrous item, rare You can use an action to place these shackles on an incapacitated creature. The shackles adjust to fit a creature of Small to Large size. In addition to serving as mundane manacles, the shackles prevent a creature bound by them from using any method of extradimensional movement, including teleportation or travel to a different plane of existence."
Does this finally put it to rest? That ain't fluff.
Here it is again:
The OR there strongly implies that teleportation is NOT extradimensional.Extradimensional Interference. Affected creatures can't move or travel using teleportation or by extradimensional or interplanar means.
Not internally consistent. Not logically rigorous.