But isn't the word "finally" there just to make clear that the Silver was the last card revealed which stopped the revealing of additional cards, because the other cards listed are not shown in the order they were revealed? I don't think it's supposed to be for comedic effect... It's striking a balance between readability and clarity of the game rules. It's important that Silver was the last card revealed, whereas the preceding list could have been in any order without making a difference.
Grammatically, it's a bit awkward to say "...2 Coppers and a Bat and finally Silver", but it's probably two separate routines. One that takes the list of all cards except the one that triggers the end of the search, giving the output "3 Fisherman, ... and a Bat", and a separate one for the last card on its own, "and finally Silver". This probably had more to do with it being easier to program this way than trying to make it funny (if this is even considered funny).