How satisfactory is the sense of closure at the end of Othello?
The way you have tagged "catharsis" in your question indicates that you want to relate the ending to this notion of purging. Let us remember that catharsis is a term first used by Aristotle to describe tragedies and the impact that they have on us. His idea was that watching the downfall and death of a tragic hero somehow enabled us to purge ourselves of our excessive emotions, enabling us to return to life better people as we have been able to express such deep and profound feelings.
Quite clearly, I think the element of catharsis you will receive from reading this play will be significanctly less than watching it. I have never actually seen a stage production of this play, and have just watched Brannagh's film version, but I can imagine that watching it would be cathartic, for we have seen a tragic hero, Othello himself, succumbing to his own fault of jealousy with tragic consequences. Given this, Othello's last speech and his description of himself as somebody "whose hand, / Like the base Indian, threw a pearl away / Richer than all his tribe..." In particular his last kiss and embrace with Desdemona before he dies is poignant in the extreme. I personally would argue that this is a very effective and satisfying ending in terms of catharsis.