Winston betrayed John Wick because he was placed in a position where shooting him was his only choice, especially because a representative of the High Table was there to see to it that he was still loyal to them. However, Winston never intended to kill John because he merely shot him in his bulletproof suit.

Winston shoots John several times, seemingly taking the assassin by surprise, and John plummets off the Continental's roof. If you take this scene at face value, it seems that Winston betrayed John in order to reaffirm his loyalty to the High Table. But that may not necessarily be the case.

Going off the evidence available so far, it appears more likely that Winston was trying to help John rather than betray him, but because they were being closely watched, he couldn’t clue John in on what was going to happen.

Winston, after reaching a no-harm treaty with the Adjudicator, unexpectedly shoots John off the roof of the Continental. John, who was presumed dead, is secretly taken to King Bower’s underground bunker. The two have nothing in mind but revenge against the High Table.