Rest-mass being a somewhat difficult concept if your particle only "exists" in bound systems, i.e. is confined. But yeah, forget the Higgs, almost all the mass you see around you is generated dynamically by non-perturbative QCD.

Edit: More explanation: If you take the quark masses as unbound rest mass, it's not clear why the proton is bound -- it would have higher energy (=mass) than the unbound constituents. This is different from atoms, as a hydrogen atom has slightly less mass than the sum of a free proton and free electron (13.6eV in the ground state).