The short answer is that Winston's death is both physical and mental: the torture he was subjected to in the Ministry of Love has destroyed his body but also, of course, has resulted in the intended brainwashing that has erased his will to resist the Party. But there is much more to it. It is a living death Winston is being subjected to, which is emblematic of what Orwell foresees, or is warning of, for the human race as a whole. There is also a parallel with Orwell's own situation as he was writing the novel since he was dying of tuberculosis and knew he had only a short time to live.
I do not believe there is any definite answer to the deeper question of whether the 'longed-for' bullet that enters Winston is figurative or literal. It is ultimately a riddle as to why O'Brien did not have Winston 'vaporized' like Syme and countless others and thus allowed him to live, for a time at least. The typical way in which the victims of Stalin's purges were executed was with a bullet to the back of the head, and the world of 1984 is an extension of the Stalinist totalitarian world. One cannot read this passage without thinking of Rubashov, the Trotsky-like hero of Arthur Koestler's Darkness at Noon, which was such a great influence upon Orwell. I believe Orwell left Winston's fate an open question, just as in some sense the fate of humanity is left unresolved. One does not know if Orwell himself really believed that O'Brien's vision of 'a boot stamping on a human face, forever' was inevitable. Some critics have contended that the appendix to the novel, 'The Principles of Newspeak' was intended as evidence that there would be a post-dystopian recovery in which man could look back on and write about the totalitarian period as an aberration (which would be similar to the approach of Jack London in his dystopian novel The Iron Heel). One can only speculate on this point, but in spite of the pessimistic tone of most of Orwell's writings throughout his entire career, I do not think he would have written 1984 had he believed the destruction of humanity inevitable. More than anything else, the book is a warning of what might come to pass, not of what must be. And Winston's 'death' whether physical or mental or both, is a depiction of what can happen to mankind if we do not act before it is too late.