Every time I read the story I find new meaning, and I suspect I will always feel as thought I am missing more than I am recognizing (the magic of Borges!) Without going into it too deeply:
Perception is a major factor in the story. The imaginary line of the Rividavia that marks the South. Dahlmann's perception of himself as two people, one travelling across the country, the other trapped in a sanitarium. (It's unclear which Dahlmann is the actual--the journey to the South may be an hallucination--but the journey is real, regardless.)
In the same way, the cat's reality is distinct from the man's, in the eternal present as opposed to trapped by awareness of past and future. The conceptual divide between man and magical beast is both imaginary and real.
- The cat is content in the moment, and not driven to seek redemption in the way Dahlmann does. For Dahlmann, caught up in the illusion of past and future, his quest reveals itself to be a trap. Perhaps, had Dahlmann been content in the present, his life would not be unraveling.
By the same token, at the very end of the story, Dahlmann is almost entirelyin the present.
Firmly clutching his knife, which he perhaps would not know how to wield, Dahlmann went out into the plain.
The remaining question about the future (will he know how to wield the knife?) will be answered presently.
Dahlmann could be understood to finally have embraced his animal nature, reduced to the primal struggle for survival. In the impending, ultimate moment, Dahlmann's identity will no longer be split between past, present and future selves: he will be one with himself.
It's possible that Dahlman's physical brush with the cat's imaginary world, distinct from the non-physical imaginary worlds of books which had heretofore been his life, awakened this potential in him.