The cars are on temporary permits. They are insured and are registered in the Czech Republic. They can be used for the duration of the permit.
I drive my Velorex here legally as well because the vehicle is over 25 yrs old so no DOT or EPA crap needs to be complied with.
By the way the Velorex is, technically speaking, mid-engine design with space-frame, using composite body panels. It has a motorcycle powertrain and sequential shifter.
Granted, it all is very primitive. As humorous as the aeronca65t's comment is (actually it is very funny and I will steal it for the use on my website-with credit of course) the true history of Velorex is not that different.
Actually, two brothers who owned a bicycle shop in Czechoslovakia wanted to build an alternative to a motorcycle and that's what they came up with. It is not known if they were intoxicated at the time though.
If you examine the design you will be surprised by the clever use of simple solutions to many an engineering challenge.
The Velorexes were produced from late 40s up to 1970. About 15,000 were produced.