Closest to that particular group would be combining Beastie Boys and Bloodhound Gang, but this is wittier. And they do it by the book, if there is one in that particular street culture. Had they done it in English and were not located in Finland, they would probably have become big.
In case you wondered, the idea of that video is to laugh at the rap/hip-hop scene... It was probably their view of Finnish hip-hop scene in the end of 1980s. "Tough" guys that play with miniature trains at home. That's pretty much my view of the current crop of Finnish metal.
And yes, that is what was back then rap/hip-hop. 10 years later they did their own version of Freestyler's music video, it was quite hilarious.