As above answers have said, Peter and Judy definitely did not seem to remember at the point in time when they meet Alan and Sarah for the first time.
However, this is not proof of them never remembering. In the original movie timeline where Alan went missing, Judy and Peter find and play the game a few months after their parents went on a ski trip and died.
In the new timeline where Alan & Sarah are married, they haven't reached that point in time yet. Since Alan and Sarah knew how Peter and Judy's parents died, they sought to deliberately change that by:
a) finding and hiring them to work for them,
b) getting them to not go on that fateful ski trip.
Either way, when Judy and Peter meet Alan and Sarah for the first time in the new timeline, their parents are planning to go for that ski trip where they would have eventually died. So Peter and Judy are still a few months away from the point in the original timeline when they played the game.
The new movie shows events where the missing person from the original timeline (Alex) returns home but seems to have deliberately not sought out the other players or attempted to change their lives. As such, the events which lead to all of them getting detention still happen. However here comes the interesting speculation and paradox part, which means that it's not completely out of imagination that Peter and Judy may eventually regain their memories of the game.
In Jumanji 2 - the Original Timeline (J2OT) -
Alex plays the game as the pilot - 'taking up' that PC slot - and goes
missing, creating the existence of the 'Freak House' tragedy.
Alex's parents donate his video game stuff to the school? where it eventually ends up in the storage.
Spencer, Fridge, Martha and Bethany (SFMB) grow up with the 'Freak House' and knowledge of the tragedy of Alex Reek
SFMB get detention and find the game in the storage and decide to
SFMB try to pick the pilot character and find it locked.
Hence they pick the 4 remaining characters.
At this point, Alex is able to return to his starting point, creating a new timeline branching out from 1996 (J2NT) and where all the paradoxes start.
Alex returns home, hence no 'Freak House' tragedy. He grows up into an adult, marries, has kids.
Alex either destroys Jumanji or he doesn't. Honestly, it would be very weird for anyone if he didn't, but since we didn't see it, we don't know.
SFMB are born and grow up in a town without 'Freak House'.
SFMB get detention and viola! The game is STILL waiting for them in the school storage area. How? Even if Alex didn't destroy it, donating it to a school seems highly irresponsible and it's not like he ever knew that SFMB were playing this game in detention.
Was the pilot character still locked? If not why didn't Fridge select that like he originally wanted to do? And if it was, then how?
And now SFMB walk down the road, expecting to see the Freak House. So post-Jumanji, they now no longer have the memories of growing up in the new timeline, their NT memories have now all been replaced by OT memories. In fact, they have OT memories even during the Jumanji game. One could say that they are actually in the OT while playing the game because clearly they only play the game with Alex.
It looks like Alex never tried to find the kids - and fair he only seems to know Spencer's full name. But since SFMB don't actually have any memories of their lives before Jumanji in the new timeline, we don't actually know for sure! For all we know, since they all seem to live in the same school district, Alex might very well be friends with some of the parents, and has spent the last however many years or months 'knowing' SFMB, while they were unaware about him or Jumanji, and he's reintroducing himself because he can see that for them all that stuff has just happened.
So! Given that in Jumanji 2, despite all the paradox, the new kids still end up playing the game and 'get back' their OT memories, but only at the right time, it's highly possible that the same could happen to Peter and Judy a few months down the line after the end of the original movie.
Of course, one possible difference is that in Jumanji, we know that Alan and Sarah have used their future knowledge to influence the new timeline in ways that directly affect Peter and Judy. However, we do not know for sure that this wasn't the case in Jumanji 2, too.
After all, despite their parents being alive, Peter and Judy have still moved to town. For all we know, a few months after that Christmas, they will end up finding the game somehow and 'play it' in the OT, and when they finish it, their NT memories of the past few months - with their parents being alive and employees of Alan and Sarah will have been replaced by the OT memories of their death and the events of the movie.
(And it is at this point in 1995 that they again throw the game away, leading it to be found by Alex's father in 1996)