I don't know specifically what happened with this guy, but here is a scenario. He climbed into the wheel well, got comfortable and hung on. When the wheel was retracted after takeoff buddy contorted himself to avoid the moving parts and ended up in some position so that he wasn't inured.
As the oxygen level thinned as the plane climbed, buddy would have gone to sleep (lost consciousness). If not completely, certainly to an extend that he was no longer in control of his faculties. As the temperature dropped and his body cooled, his state of mental acuity lessened further as did his body's ability to maintain a reasonable degree of thermal regulation. His brain decreased his metabolic rate in response. It's an autonomic process.
How long the brain can be deprived of sufficient oxygen before being irreparably damaged is a function of how fit the person is, how cold the environment and how much oxygen is present in the air being inhaled.
Because we fly often, we can reasonably assume from personal experience that as the plane lined up for its approach to Miami, it steadily descended in altitude eventually passing the 10,000 foot mark. The plane probably began descending before beginning its final approach. As the plane descended, more oxygen became available as the wheel well is not a sealed airtight compartment. As the available oxygen level increased so did the ambient temperature, albeit slowly, but steadily.
Usually jets line up with the runway using ILS and follow a glide scope path to the ground. This process can take 10 minutes or more. At some point, oxygen levels and temperature were sufficient for buddy to wake up or shake off the cobwebs of reduced capacity and he was able to or was just lucky not to fall out when the wheel was extended or thudded on the runway.
Exactly how long someone can survive these conditions probably varies with the individual within some sort practical minimum/maximum limits. From SD to MIA, this guy did it. Would the result be the same if the flight had vectored around a storm adding 15 or 20 more minutes to the fight? I don't know.
Buddy was lucky. He would not have been keenly aware of his situation for most of the flight but did have enough time to wake up so he could hop out when the plane stopped at the gate. Someone else might not be able to duplicate the experience with the same result.