This is because his past has already changed.
In the 'original' timeline, Picard himself challenged the Naussicans to a rematch, and re-rigged the table to beat the Naussicans.
I see two possibilities from here for this original series of events.
- The Naussicans accepted, were soundly beaten thanks to Picard's intervention, and the next day confronted them about the cheatery, leading to the fight.
- Picard issued the challenge, and the Naussicans agreed to a rematch the next day, extending his 'dead'line by an additional day.
Either one of these circumstances would make Q's statement true when he said it, but Picard's own meddling changed those circumstances. In the episode...
Picard refuses to take part in the plan to trick the Naussicans, and even prevents his friend from trying to rig the Dom-Jot table, threatening to report him to Starfleet. Since neither he nor his friends challenged the Naussicans and set things up for a rematch, the Naussicans, based on the events of the episode, assumed that the Federation cadets were cowards, and returned to the bar to taunt them.
Basically, by interfering with the way things originally went from his memory, Picard altered the events of his past, and in doing so unexpectedly caused a confrontation with the Naussicans to happen a day earlier than expected, under completely different circumstances.
This is possible because Q allowed Picard's actions to have reprocussions on his own life - it's even possible that none of this happened at all, and that Picard was merely hallucinating these events. Because of the nature of Q, we will never know.