'Platinum' in this sense, is arguably a proper noun. It means "a card named 'Platinum'". It's even capitalized in the game log. Usually, in English, the convention is to pluralize proper nouns simply by adding an 's', ignoring whatever other conventions might exist for common nouns.
By adding "s" or "es," yes. Dominion has some fun examples. I gave him eight Ruinses, then bought out the Nobleses.
However! The rule doesn't come up much for most people. But for gamers, for a few decades now, it has come up plenty. And this group has not chosen to follow that rule; they pluralize the proper nouns as if they were the thing they refer to, leaving them untouched if already plural - my deck has 4 Llanowar Elves and 4 Cities of Brass, not 4 Llanowar Elveses and 4 City of Brasses.
Since they're the ones actually pluralizing proper nouns and that's how they do it, the trend is for that to be the new rule.
None of this affects Platinum of course. I think when people started saying Platina they were just being silly; if not, man, guys, what? Some people now though may be used to seeing people saying Platina. The actual plural is of course Platinum, or if you want, Platinums. But people saying Platina do communicate clearly.