If this is level with the rest of the floor, I suspect that there was one layer of mat or even chopper gun material, and some sprayed on gel coat. The boats are laminated in the mold, with gel coat, mat, roving / mat alternate layers on the bottom outside. Then the end grain balsa core, finally it should be a few layers of mat and cloth, or even a layer of roving. But on my C Dory 25, there were areas which were just one layer of mat--and then gelcoat.
My suspicion is that what you are seeing is the end grain balsa. However, the red stripes are a little puzzling to me. Can you easily stick a tooth pick or even an ice pick into the wood? Is the wood wet?
There aren't any stringers in the bottom of a C Dory 22. It is also possible that there is clear resin, and a layer of mat and cloth--and that the bottom was gel coat/paint which did not adhere well.
First we need to find out what the composition is--and then probably you will need to add another layer, and re-paint. You might even consider truck bed liner as the finish coat for the cockpit. It is essential that the wood be sealed.