That is not correct. The current Super GT NSX GT500's are all naturally aspirated. The JGTC GT500 NSX's in that video are also NA. They converted to 3.0 liter turbos for two years with lackluster results, and then went back to 3.5L NA, only this time the now longitudinally mounted engine sits in an all carbon chassis that no longer shares any components with the original NSX. They also have a much deeper baritone exhaust compared to the previous NA versions.
In actuality, the NSX's in that video are more similar to ours than you think. They share the same aluminum chassis (albeit reinforced) and same transversal engine layout. The obvious differences are a 3.5L displacement, dry sump oil lubrication, exotic engine components and aggressive cams and overall compression, etc etc. Engine pitch is also affected by other factors besides RPM's.
In my opinion, the previous generation GT500 NSX's sounded the best, even thought the newer longitudinal ones have a lot more torque and are much faster.
ps. There are a lot of threads here going a ways back discussing the physical attributes that differentiate engine sounds between the NSX's, Ferrari's and the like. One thing I've noticed since Ferrari switched to 4 valves from 5 among other things, their engines became a lot stronger but deeper in pitch as well. Just have a listen to the F430 or the Enzo.