The fundamental plasticity mechanisms in thin freestanding Zr65Ni35 metallic glass films are investigated in order to unravel the origin of an outstanding strength/ductility balance. The deformation process is homogenous until fracture with no evidence of catastrophic shear banding. The creep/relaxation behaviour of the films was characterized by on-chip tensile testing, revealing an activation volume in the range 100-200 Å3. Advanced high-resolution transmission electron microscopy imaging and spectroscopy exhibit a very fine glassy nanostructure with well-defined dense Ni-rich clusters embedded in Zr-rich clusters of lower atomic density and a ~2-3 nm characteristic length scale. Nanobeam electron diffraction analysis reveals that the accumulation of plastic deformation at room-temperature correlates with monotonously increasing disruption of the local atomic order. These results provide experimental evidences of the dynamics of shear transformation zones activation in metallic glasses. The impact of the nanoscale structural heterogeneities on the mechanical properties including the rate dependent behaviour is discussed, shedding new light on the governing plasticity mechanisms in metallic glasses with initially heterogeneous atomic arrangement.