Goons says: "While this is in play, when you buy a card, +1VP". When you play Procession on Goons, Goons is in the trash and no longer in play. So, you don't get any VP tokens for that.
However, it's not actually trashed on the first one, since it has to be in play to do the second play....shouldn't it at least give points for the first play? {ed: although I guess that might be tricky since the points come from the buys--which is why maybe you should get all points from buys available before it is trashed, in this case 3}
Looks like you're missing a key aspect of Goons... which is that it does NOT give you any points due to the fact that it gets played. It doesn't matter how many times you played Goons, there is no "points for the first play" or "points for the second play". Goons only gives points based on "while this is in play." "In play" is completely separate from being "played." Yes, usually cards that are "played" end up "in play." But there's lots of exceptions such as Feast, or cards played with Procession. In the same way, if you Throne Room a Goons to play it twice, you will still only get ONE vp each time you buy a card, not two, because there is only one Goons in play.
The version of Goons you are thinking of is much more powerful than the actual Goons, because you can get a lot of VP from playing Throne Room-Goons or King's Court-Goons, even if you don't actually buy any cards.