I ought to be cautious here after just one reading of Anna Karenina, and having no knowledge whatever of Tolstoy criticism; but I'll shoot my mouth off instead. I do not see how it is possible to discuss Anna Karenina at the length Geoffrey Macnab does in this column - in which he is assessing various filmed versions of the novel - and say nothing whatsoever about the 'other' story in the book, Levin and Kitty's. The love between Anna and Vronsky is obviously central. But to my eyes Tolstoy's exploration of its development, its different shapes and phases, Anna's and Vronsky's changing perceptions of their situation, has as its essential counterpoint the consciousness of Levin, his relationship with Kitty, and his thoughts about the meaning of life (including family life) and death. Lop that off and you have a different and much impoverished book.
(Incidentally, I don't share Keira Knightley's quoted view that Tolstoy 'hates' his own creation, Anna. If he'd hated her, I doubt that he could have traced all the nuances in her relations with Vronsky as well as he does.)