The closest I found in the transcript of the talk was this piece:
MR. BROOKS: So something like a guaranteed minimum income for people who
are working full time through an expansion on the EITC or a wage subsidy seems like the
right way to go.
MR. GATES: Yeah, one of my favorite AEI papers – I didn’t get time to look it
up last night
Right, he seems to be saying that instead of a minimum wage that corporations have to pay, there should instead be something that looks like a minimum wage to employees, but where employers can pay as little as they like and the government will make up the difference between that and the minimum, but if you don't have an "employer" or they don't certify that you've "worked" sufficient hours, you don't get the subsidy, either.
So, like a basic income, except that you have to swear fealty to an employer to get it. I see one of two possibilities:
(1) Either the restrictions on qualifying employment are tight enough that it serves as a subsidy for select existing operations and a competitive disadvantage to new business with smaller scale (because of compliance costs) or new models (because of regulatory assumptions), or
(2) The restrictions on qualifying employment are so loose that this is basically unconditional basic income with a whole lot more administrative costs and failure modes that exist just to satisfy the desire to create an illusion that it has something to do with "work".
MR. BROOKS: So something like a guaranteed minimum income for people who are working full time through an expansion on the EITC or a wage subsidy seems like the right way to go.
MR. GATES: Yeah, one of my favorite AEI papers – I didn’t get time to look it up last night
Source: http://www.aei.org/files/2014/03/14/-bill-gates-event-transc...
Edit: after re-reading it, I think this has nothing to do with basic income since it's for people who are working full time.