In each Savvidy domain, the chromomagnetic field has a random direction - both in space and the color space. So of course, in a domain, both the SU(3) gauge symmetry as well as the rotational symmetry is broken. However, the domains change randomly, so the average direction both in the real space and the color space is "nothing"; so one can't say that the situation is equivalent to the Higgs mechanism.
The Savvidy model is a model for confinement - in particular, for the confinement-deconfinement phase transition. In particular, the Polyakov loop - the monodromy or Wilson loop around the Euclidean thermal time direction - is the order parameter that behaves discontinuously near the phase transition. This behavior may be approximately calculated in the Savvidy model.