In the first part of his review, Eagleton gives a sketch of Bakhtin's difficult life under the Stalinists. At one point, he writes:
Here [in St. Petersburg], as always, he was surrounded by a close group of anarchically minded writers and eccentric polymaths. Indeed, the story of his life is the tale of one such coterie after another; they seemed to form spontaneously around him in whatever godforsaken backwater he happened to wash up. He was a man who practised dialogism as well as preached it. By the late 1920s, however, the kind of religiosity which his circle promoted [a form of Russian Orthodoxy] was in increasing disfavour with the state; and in 1929 Bakhtin was arrested for membership of a religious circle, anti-Communist proclivities and corrupting the young by his teaching.
If you think this sounds suspiciously like an ancient gadfly featured in Bill and Ted's Excellent Adventure, you'd be right, for that is the connection Eagleton goes on to make explicit:
The thinker whose notions of dialogism, subversive irony and indirect speech ran back to Socrates now seemed about to suffer his predecessor’s fate.
But he didn't. To find out why, you can read the rest here.