Recent update.
Just inspected another R33 gts-t today. The last one was stick, this one was auto. This time, I had the guy drive it for me and show me the car's response when boost kicks in. Being a cold and rainy day today, he drove around normal to warm it up a bit for about 5 min. After that, he switched the selector gear to "2" and went the way through with it. Being a stock car, boost kicked in at 3000rpm and it held on till around 5500rpm when he let go. ( was in a residential area, so can't boost it all the way.)
Though being auto, when he was driving it normal in 1st and 2nd gear, the car feels like absolutely normal like it should. It didn't have that weird draggy feeling the first one had. Some of the guys here suggested a bigger turbo being installed into the first car. Possible, but imo it shouldn't affect the performance below 3000rpm. The first car felt like it was towing a bus at 1st gear and this one feels totally alright. So back to the first car, I would suspect that something somewhere needs an eye on it and the owner is either hiding it or not knowing it. Feels like a clutch or gear slip, but can't confirm.