I saw that particular video several years ago. I remember thinking how funny and amazing it was that he showed up as if he were going out for dinner, with his loafers on no less! Such a talented driver.
Acura was a brand created for the N. American market (although recently expanded to Hong Kong, Mexico, and China). Elsewhere in the world, the NSX was branded as Honda, as can be seen from the nose badge on this car.
I suspect that the re-branding to Acura in N. America was to do with the strangely low regard people have for Honda in the US. Coming from the UK I can say that in Europe too, the first Hondas were regarded as something as a joke, but when they moved on, the public opinion moved on also. I really don't think they're held in significantly lower regard than Toyota in Britain.
I really don't get the negative image they have in the US. Sure, their first cars were laughable, but that was the past. Personally, I'd rather buy a Honda than all but a few US cars.