We present a quantitative analysis of the nonequilibrium assembly of colloidal particles dispersed in a nematic liquid crystal. The driven particles assemble into reconfigurable circular clusters by liquid-crystal-enabled electrokinetic phenomena generated by an AC electric field that provides propulsion along the local director. We identify the coexistence of different aggregation states, including a central, jammed core, where short-range elastic attraction dominates, surrounded by a liquid-like corona where particles retain their mobility but reach a mechanical equilibrium that we rationalize in terms of a balance between centripetal phoretic drive and pairwise repulsion. An analysis of the compressible liquid-like region reveals a linear density profile that can be tuned with the field frequency, and a bond-orientational order that reaches a maximum at intermediate packing densities, where elastic effects are minimized. Since the phoretic propulsion force acts also on assembled particles, we compute the mechanical pressure and show that a hard-disk equation of state can be used to describe the assembly of this driven system.