It had a market where consumers could choose to spend their money on particular brands of consumer goods, with varying degrees of quality.
There weren't a lot of different brands, but there were some, and they were in direct competition with eachother. The bigger issue was overall low productivity and high logistics friction, which leads to shortages (and a MIC that sucked up half the country's productive output didn't help matters).
Sure, but is competition an ideological construct? Even the Soviet Union had competition between companies and institutions – without any free market.