I dunno, it's pretty hard to strip ink off a playing card. I could believe they were submerged for a long time and survived. In terms of 'what they went through', really they just got wet. You take them out and dry them.
I think its interesting they were on there at all; somebody brought them over to London and was bringing them back to NY. You could buy cards in England (dunno about USPCC but I'm guessing not usually) but somebody stuck with their Steamboats rather than just buy a deck over there.
They got wet - and stayed wet, for over eighty years! When you're talking about that length of time, decomposition of the paper itself becomes a factor. In terms of breaking down to base components, a traffic ticket has a "half-life" of about 1.5-2 weeks; I can't imagine a playing card lasting too much longer than a traffic ticket, even with lamination. Sure, there's the laminates protecting the cards, but even so - over eighty years... I don't even think the corpses of the dead survived this long.
I'd guess they were tucked into a drawer in the furniture of some cabin somewhere at the very least. If they were simply on deck somewhere or in someone's pocket, they'd be scattered all over the place and nearly impossible to find. Somehow, somewhere, they were protected from full decomp and exposure to the bacteria that would normally break down the paper. The depth and the cold of the water may have been factors as well.
And yes, it is cool to think of some person taking their trusty deck of Steamboats all the way from America to London, and on the voyage back.