As was stated earlier, the spare tire is located under the cargo area and appears to be a temporary spare. I was able to snap a (low quality) picture at the Indy Auto Show last week.
I think there may be some confusion on what a "full-size" spare is.
Dominick Infante in the posted video, as well as pictures from the auto show floors, show that the spare is a "full-size" donut / temporary tire. On any AWD Subaru with a spare, the tire needs to be "full-size" in regards to circumference due to the all-wheel drive system mechanicals.
Just like on a current Forester or Outback, the tire is equivalent in circumference / diameter to a normal tire, but the width and tire design are not the same. This spare does not appear to be acceptable for off-road use or towing, as it is still a donut / temporary design.
A conventional "full-size" spare would be equivalent in tire circumference, width, and design to allow no degradation or limitation of performance when changing to a spare tire.
Since the spare is mounted underneath the vehicle in the Ascent, there is a good possiblity a real full-size spare would fit. The increase in width compared to the donut would mean that the tire would hang down lower, which could hurt departure angle or appearance from the rear (if the tire shows below the bumper). The next question would be if the mounting hardware would work with the wider wheel / tire, but it may be not too difficult to make work.