'What, in this context, does "Stalinism" mean?'
I explained in the article, in the 8th, 9th and 10th paragraphs, the section that begins 'Communism as a movement grew alongside and out of the class struggle... and end '...the most forward-looking and militant people in the 1930s and 1940s were left championing the cause of the most reactionary and destructive regime.'
Stalinism means pretty much what it always meant to those that coined the term. Stalinism was a worldwide political movement arising out of the decay of the Communist International. Stalinism means the transition from an internationalist perspective, towards one based on the defence of Socialism in One Country (namely the USSR), the policy that Stalin advanced in 1926. This was the policy that transformed all the parties of the Communist International into a defensive posture of 'defending the gains' of the regime in Moscow - though of course there were no gains: Stalin had turned Russia into a slaughterhouse, where tens of millions were sacrificed through famine and repression to die early deaths.
Stalinism was the policy that dominated Hobsbawm's life, since it was in pursuit of that goal that he became a defender of the betrayal of the Spanish Republic, then a champion of the British Empire (once Stalin broke with Hitler), then a defender of the Soviet invasion of Hungary, and finally a champion of the new realism policy of the Labour Party leadership in the 1980s.
Chuck asks whether any of this ancient history matters. Well, no, it doesn't really, except that Hobsbawm is an historian, and his best-selling history Age of Extremes is a boiler-plate apology for the most vicious betrayals that the Stalinist movement made. As long as Age of Extremes remains a point of reference then historical truth demands that its many outrageous misrepresentations of history are explained.
James