No poet, no artist of any art, has his complete meaning alone. His significance, his appreciation is the appreciation of his relation to the dead poets and artists. You cannot value him alone; you must set him, for contrast and comparison, among the dead.
While the passage (shown with its following sentence, above) does suggest a need to understand where the artist stands among earlier poets and artists, it says slightly more than that. It asserts that comparison to those gone before is a structural requirement for criticism; ie, that such comparisons are not merely helpful for understanding, but are a requirement for meaningful comment.
That aside, his appears to function possessively in its several instances.