Will there be another giveaway for the people on the first 2 pages of this again?
The "top user swag" offering to the first two pages of users is usually a one-time offer per site. It is (also usually) done shortly after the site graduates from beta, and it is intended as a bit of a celebration for folks who were there in the early stages of the site and saw it to a full launch. Arqade actually ended up with two swag offers. The second followed the site redesign/rebranding that happened last year.
We have no plans to re-run swag packs at this point. We did several years worth of anniversary gifts for Stack Overflow, since it's still our flagship site, but what we found was that the top 2 pages of users are fairly static, so we end up gifting things to the same group of people over and over and unfortunately leaving other folks in the dust. The "top 2 pages" model just doesn't work in the long term.
We do have swag available for things like community-driven site anniversary contests or other events that involve the site's community, so if you guys want to organize something, let us know and we'll be happy to provide t-shirts, stickers, etc.
While I don't have a definite time frame in mind, I would say that it will be a little while before we do another mass swag send out for Gaming. With other Stack Exchange sites launching and graduating from Beta at an increasing rate, getting swag packs out to new sites has taken priority to sending out follow up swag packs. Again, that's just my understanding from passing remarks made in meetings (no meetings have been focused on this topic, though, so I don't have in-depth info; also the Community Team probably/definitely knows more about this than I do).
And bwarner is correct about building up rep. There are going to be plenty of opportunities to take part in the gaming promotional grants this Fall, and the higher your rep the more likely you are to get a game.
Unlikely (especially since it would largely be the same people). However, the Promotional Grants also give preference to people with high reputation, so if you're looking for motivation to keep building up your rep, it will definitely give you a shot at free games.