FJ 1200 engines I think
Those look like a similar thing to Legends and Dwarf cars here. The two series I have looked at attempt to level the playing field by using horsepower limits, and run dirt ovals. I have a hazy recollection that some are run on asphalt, but I think they were still round tracks.
I think the biggest problems for running motorcycle engines in street cars is the difference in emission standards and balancing NVH/safety concerns with the "added lightness" necessary to make the tiny engine feasible.
I don't really believe that the dinky-engined cars we have now are under-designed from a power perspective... just that automotive design priorities and limitations do not allow the manufacturers to take advantage of the design items used to make power in motorcycle engines.
Plus, can you imagine the public perception of a car that has the teething/break-in issues a new motorcycle has?