The kind of reward system you're describing already exists on Area51:
When a proposal enters the commitment
phase, you can earn reputation by
referring users to the proposal:
Referred user commits to the
proposal +5 Referred user participates
in the beta +25 You earn the most
reputation when a user follows through
on their commitment, and that extra
reputation won't count towards your
maximum reputation per day.
I think you're suggesting that you should be able to generate the referral points on the specific beta site (Gaming) rather than A51, which would seem to make sense given that the user base there will increasingly tend to have no connection to A51.
The easiest approach to what you're asking would simply be to create an identical system, but with a different referral link connected to the site. Then, If you use the referral link from the Gaming site, say, you'd get the referral points there, rather than on A51.
But there's a major flaw there, which is why (I think) you currently only can get badges on the actual beta sites for referrals: While referring active users is desirable activity, the number of users you refer is not a good proxy for how much the community should trust you. If you award meaningful points on the Gaming site for referrals, you could essentially get to moderator-like status without demonstrating meaningful expertise or contributing to the dialogue.
I'd be inclined to leave it as is.