Why is rolling friction a type of static friction even though static means not moving?

It's static because the major cause of rolling friction is deformation of both roll and surface it's moving on - surfaces do not slide on each other(at any given instant the relative velocity of point on the roll that touches surface and surface itself is zero - at least in the model). The deformation causes the point of contact to be slightly displaced in front of the moving roll and reaction force at this point plus weight of the rolling object are no longer on the same line. This introduces torque that opposes the rotation of the roll. Rolling friction is essentially static friction because the point of the wheel in contact with the ground does not slide against it, but instead maintains its position. If enough static friction does not exist and the wheel slips against the ground, motion will not be proper. Sliding friction will however be taken into account in that case.