While there's reference throughout "1984" that many people who confessed to supposed crimes and had become thorough believers in Big Brother were then literally executed, it's deliberately not made clear whether this was the fate of every one of them. Similarly, the ending of "1984" is far from making clear whether that's Winston's literal fate, at least during the last scene in the Chestnut Tree Cafe. If anything, it makes clear that the "bullet" that enters Winston's brain at that moment is allegorical, since he experiences it while imagining himself once again in the Ministry of Love, while he's actually still seated at the table in the cafe, and a moment later he's still alive in the cafe, with tears running down his cheeks, and inwardly expresses his love for Big Brother. It's possible, as others suggest here, that this is merely the precursor to his actual execution later--first a metaphorical bullet, followed some unknown time later by a literal bullet. It seems likely that Orwell left the ending somewhat ambiguous, because Winston's particular fate was meant to be seen either way, or both ways at once. The earlier descriptions of literal executions was sufficient to show that the state would carry out such real executions on some people, while Winston's experience in the cafe may have been meant to show they also might have carried out purely psychological executions on other people; and for still other people, they might have first performed the psychological execution, and then some time later, the literal execution. All options were either at the whim of the state, or (more likely) based on detailed examination of what would work best against the subject, and/or for the state.
During Winston's brainwashing/torture, O'Brien makes contradictory statements about the state's plans for Winston, which to me implies neither Winston nor we are meant to know for certain what Winston's fate will be. After O'Brien tells Winston that party originators-turned-traitors Jones, Aaronson, and Rutherford were definitely executed after being successfully brainwashed, there are these exchanges
'Does the Brotherhood exist?'
'That, Winston, you will never know. If we choose to set you free when we have finished with you, and if you live to be ninety years old, still you will never learn whether the answer to that question is Yes or No. As long as you live it will be an unsolved riddle in your mind.'
'Do not imagine that you will save yourself, Winston, however completely you surrender to us. No one who has once gone astray is ever spared. And even if we chose to let you live out the natural term of your life, still you would never escape from us. What happens to you here is for ever.'
In other words, we're supposed to be left as unsure as Winston about the exact nature of his execution--kind of a quantum uncertainty.