[carlr]

The solid 1,500-mile-wide inner core, which is surrounded by fluid, rotates about one-quarter to one-half degree more than the rest of the world every year,

Not that unusual.I presume the Earths rotation begins at its core and since that is surrounded by fluid there is bound to be a loss of efficiency as it transmits the rotation up to the solid mantel.
The torque converter in an automatic transmission has the same thing happening as does any fluid coupling.The energy that is not transfered directly to what it is driving is lost in the form of heat.

[Oztrich Boy]

No it works the other way around.

The rotation continues because of inertia

But tidal braking from the moon slows it dowm. This is greatest at the surface. So the crust slows and that slowing is transmited through the mantle to the core.

So the core isn't spining faster, the surface is spinning slower.