Yes, but see below.
> If Activision's version of this piece of paper was chewed up by rats in the 90s, does their ownership stake vanish in a puff as well?
No, but complex. Legally the contract is still valid, but they still need to show the court what the details are. All parties to a contracts get a copy, and so Activation can legally force other people who should have a copy of the contract to produce it, any copy is enough (or several partially rat eaten copies may be enough to reproduce what the original said). Activision has all the time they want to find copies of the contract (unlike trademark, copyright isn't use it or lose it), so you are risking the above for a long time. Sometimes enough testimony in court of we did have a contract is enough - when it is obvious there must have been a contract at one time the court will put together obvious details which might be enough to sue. In this case the 3 parties can agree that while they don't know who as rights between the 3 of them the rights must be contained and so they can agree to a 3-way split for purposes of going to court - even if it latter turns out only one party had rights, that party agreed to the split (though if you years latter can prove a 4th party has rights they can sue the other 3).
Of course if rats did eat all copies of the contract the lawyer fees to figure this out are likely more than the game is worth and so it probably isn't worthwhile to sue, so practically it may be as if they no longer have rights to the game just because they can't afford to enforce it. This is a very risky take though and so nobody should risk it.