I didn't pick up the number of available slots, although the article does mention that 13,000 applications were handed out. When there are that few actual slots available, I don't believe the applications have anything to do with who wins. It's got to be personal contacts. I don't believe that the bureaucrats are going to wade through 13,000 applications in some merit-based evaluation process. Maybe it's something like "the thirteenth caller gets the freebie" announcement on the radio, which would be more fair than what I suspect actually happens.
Section 8 is income-based. The government pays for part of your rent, based on what you earn (or don’t, as the case may be) and what the rent is. Some people get a full ride, and some (people who actually work, sadly in the vast minority) get only a percentage. What the tenant pays is based on 30% of your income.
Say your rent is $1395 a month. If you make, say, $2700 a month before taxes, you’d pay your landlord $810 and the government pays the other $585.