(And, indeed, one could even make a case that "after you finish gaining" would mean after all when-gain instructions have been carried out, i.e., not the same as "when you gain".)
Uhm. Since "when you gain" is the same as "after you gain", I guess you're saying that the word "finish" makes a difference? So when you have gained a card, it's after you gained it, but you're still not finished gaining it? You're at a point when it's after you did something but you're still not finished doing it. I think you'll agree that it doesn't make much sense.
Specifically, I mean that this is an issue of
aspect. English has different grammatical ways of indicating how the meaning of verb interacts with the flow of time. Using the simple present, as in "when you play a card", typically portrays the verb as having a
punctual aspect. So in "when you play a card", 'playing' is something that is construed as taking place at a specific point in time (here, the point at which the card enters the play area), not something extended over a period of time.
Putting a verb in the gerund form with
finish, however, implies that it has an
imperfective aspect—i.e., that it refers to something that takes place over an extended period of time, with a beginning, duration, and end. In that case, the period of time over which the action of 'playing a card' takes place begins when you start moving it toward the play area, and ends after you finish executing the relevant abilities, at which time you're done playing the card and can play another card, or whatever.
So yes, I do think that the word
finish makes a difference, because it forces an imperfective aspectual interpretation on the verb it governs, whereas the simple present encourages a punctual interpretation of it.