I am not sure that this is a fair interpretation of the Radical Chains' politics. They are influenced by the Russian emigre Marxist Hillel Ticktin, whose critique of the Soviet plan is far from turgid, but on the button. I do not believe that they are opposed to planning per se, but as the quote you cite says, opposed to planning that is not on the part of the associated producers. (That said they do tend towards the anarchist interpretation of Lenin, as I remember.) There was a Mark Etkind who sold Radical Chains when I was at college. The last I heard of him he was collecting money to go to Russia. The magazine featured writers like Ticktin, the undersung Scott Meikle as well as some great archive stuff, like Noah Ablett's dialogue with a marginal economist. Cranky, but some good stuff in there.
Soviet workers were indeed involved in a 'struggle against the plan' throughout the greater part of the USSR's existence, but sadly their struggle was on the basis of their own atomised existence under the soviet system. Hence the 'struggle against the plan' was largely a matter of absenteeism, private endeavour and so on.
McNally's book is ok, but it is pretty timeless. It came out in a period of resurgence in the reputation of Hayek (who is made to stand for capitalist ideology tout court). That was just at the point of the collapse of the Soviet Union, when capitalist triumphalism was endemic.
But today, such capitalist triumphalism is hardly the central message of bourgeois ideology, which is much closer to what Georg Lukacs called 'negative apologetics', ie a gloomy dismissal of all human endeavour, rather than a capitalistic boosterism.
-- Jim heartfield