But is it even possible to add such a huge mechanic to the game? Actively changing a fixed card cost based on the actions on the field?
I'd imagine it was pretty simple, actually:
Each Wyrm would have a variable assigned to it when it appears in your hand. When a card is played, that variable would decrease by 1. Each turn, the variables are evaluated and the card's cost is shown. (Similar to Chimera the actual stats won't appear until you play the card - you'd have to figure that out yourself but in this case it's pretty easy to tell.)