I remember him specifically mentioning that it was a baseball game (like a video game), that the game had stopped working/was accidentally damaged, and that it was to waste the enemy's time as any trash thrown overboard was being picked up and gone through for any potential intelligence benefit, meaning that they would have likely had to have piece the entire thing back together.
My friend, who was my roommate at the time, says he recalls him possibly being on a carrier. It would have been around 1975-1980.
This is a fairly doubtful story.
Classified information remains (shredded paper, ashes, disk fragments) are not disposed of in a way to make it known they're classified specifically for the purposes of making it difficult for someone sorting through materials to identify what might have some value.
I wouldn't entirely rule the story out as someone having a "good idea" though. However in terms of military deception techniques, it's a pretty poor one. When planting false or deceptive documents, it's important that it be believable (or, a folder with "TOP SECRET NATO BATTLE PLANS DO NOT OPEN ESPECIALLY NOT RUSSIANS!!!!!" left on Putin's doorstep is a bit too on the nose to be trusted by most intelligence organizations). Dumping a clearly "classified" container in an environment in which it may be expected to be collected by Soviet intelligence is again, just too obvious.
The technical ability to reassemble disks is also questionable within time frame. Somewhat famously the USAF had to invent a mechanism to put floppy type discs together in 1991 to investigate a murder committed by a service person. It's possible the technical means existed within the intelligence community, at least as far as "known" capabilities, cut up magnetic storage medium that's spent time in salt water seems like a tall order.
As I mentioned in point 2, this is still an entirely possible story in the sense that it might have been someone getting "clever" or the classic military "good idea fairy" but at the least, it makes very little sense from the sensitive materials handling, military deception, or technical exploitation perspectives.