Why is the actual dihedral angle of gauche butane different from
60degrees?

The actual dihedral angle of gauche butane differs because of a phenomenon known as steric effect.

Explanation: Steric effect is phenomenon that influences the shape and reactivity of ions and molecules caused by nonbonding interactions.

Steric effects goes with electronic effects, which usually tells the shape and reactivity.

Steric effects is a result of repulsive forces between overlapping electron clouds activities. These steric effects will even distort angles and molecular geometries.

In the context of butane, because presence of two bulky methyl groups (-CH3), the steric interference occurs which causes the methyl groups to be some what far apart hence, increasing the dihedral angle between the two methyl groups which in turn, affects the dihedral angles of other groups present in the molecules.

Therefore, the dihedral angles between the hydrogens are not exactly 60 or 180 degrees.