I was at a fall festival where you could ride pedal cars like the on in your link. There was a little unpaved circuit to ride them on. I had a ball pedalling them. I was in shape from cycling regularly so I lapped everybody. I felt they were plenty sturdy.
There are some web sites where they build adult gravity cars. Most look like mini hot rods. One particular gravity car club requires that your chassis be based on a hand truck frame. I would rather start with the pedal car in you link.
I had been seriously considering building a velomobile with electric assist, which would be street legal (if it has 3 wheels). It is basically a reverse, or tadpole trike with a body kit. I soon realized that driving a velomobile on my local roads would be very dangerous, especially during rush hour.