Marvin needs 1000 pieces for the machine.

As pieces do not appear in Marvin's game, it is clear this mechanic was added later than 1997 but before 2000.

Presumably, given Rainer's note in the CARE A Description, Rainer had finished the caskets (the censored versions), added the Care pets and added the pieces.

Now, this rebuilt version of the game (which seems to have Marvin entombed) would need to be test run in the same way the original game was so who does Rainer call upon, the only person to beat the original game, Belle.

Belle and Rainer collect the pieces and put Belle into the machine to test run it or they collect the pieces and Marvin puts Belle into the machine, intent on rebirthing her as Tiara however Belle quits the game and something goes horribly wrong. A corrupted amalgamation is born and banished to the quitter's room in panic, Rainer finishes the game, sends it to the family at Xmas 2000 and kills himself (it's possible that the reason for this is for feeling responsible for entombing Belle, you could say that she and Rainer were psychologically damaged after the rebirth, Tiara might say that anyway).

However, the main point is that it's impossible for Marvin to complete this objective. It requires two other players to collect 500 pieces in their respective games and insert them into the machine. Which means one of two things;

1. This was always the intention, which means that Anna and Care were likely the two people gifted the game that Xmas and were present when Rainer did his farewell act. Which would imply that Rainer's gift was to allow Anna and Care to work together to potentially free or see Marvin or even just claim some kind of closure on the whole ordeal, rather unclear admittedly.
2. That originally Belle collected 1000 pieces. The rebirth of Belle went haywire and as a fail-safe, Rainer changed the code to allow only 500 pieces to be collected in a single playthrough so that it can never be attempted again and explains why Belle was imprisoned and it took a forced glitch reboot to free her. Belle then collects her pieces again as seen in P12, Paul gets his and they work together to go back in time (enter Marvin's original build in the demo sequences and complete the rebirth but they mess it up again, the end, credits... really? Probably not. Anna and Mike's key roles are yet to be explained.
3. A combination of both.

EDIT: I just want to clarify that the pieces in Even Care were part of the game's initial design and when I refer to Marvin not having them was more in reference to them being in the Newmaker Plane specifically for the rebirth machine. Rainer implies that his caskets are incomplete but will be finished so he certainly was planning these changes before his Marvin scheme detoured him. He probably wanted to bring back Mike as initial goal, maybe even setting Care up to be the one rebirthed. I know it's in a game and not real but we see the confusion Tiara/Belle has brought forth.