I clicked on the English version of the web page and there is no mention of type-r anywhere in the ad.
You can view the English version here:
http://www.goo-net-exchange.com/usedcars/HONDA/NSX/700120009320120411001/index.html
In the comments it says ordinary engine not a type-r engine.
Where did you see type-r mentioned?
I really don't know if type-r's came with a black engine bay and the rest of the car painted white.
Why Honda would go to the expense of painting an engine bay black then painting the rest of the car white doesn't make a lot of sense to me.
Judging by the pic of the engine bay you can see what is either white wrap or poor masking around the bay.
The dash work also looks cheesy and poorly done.
I'm not sure why an owner of a rare type-r would mess up the dash like that.
I also notice the rear fender bolts aren't painted white so maybe the car has been wrapped.
On the other hand the front compartment is white.
Maybe it's been repainted but why would Honda paint the front compartment white and the engine compartment black?
However I am not that knowledgeable about type-r's so you may be correct that Honda painted the engine compartments black and the rest of the car white.