Okay, the first photos look photoshopped.
Or maybe a concept car that doesn't go anywhere.

If i was doing such a thing, the first thing to go would be two front seats.
The wheel, and the holding mechanism (struts, tie rods, A-arms) take up the entire space where your feet would normally go.
There is none of these things shown, just the wheel. So, either they are all gone, tying the wheel straight to the frame (which makes for a very bad ride) or its just for show.

More tires provide more traction which means faster acceleration but with more stability.

This is untrue. The larger the surface area of rubber in contact with the road is the upper limit of how much force you can apply for acceleration. But really, the first dynamic is how much downward force you have on the driving wheels. Further, breaking the rubber grip is usually only noticeable off the starting line.

And with the weight transferred to the back under acceleration, four front tires mean nothing.

Four front tires also greatly reduces the risk of hydroplaning.

This is blatantly false.
To resist hydroplaning the cars weight has to push the tires down through the layer of water. Weight divided by 6 is less than weight divided by 4. So, the car with 6 wheels would be much more likely to hydroplane.

But, there might be something about having the two front tires push the water out of the way for the next two tires to grip.

Lastly, if 6 tires really made a difference in track handling, the 24 hours at Le Mans would have all 6 wheeled cars.