From the looks of it the transom plywood has been water through the layers for a while. i wouldn't worry about this to the extreme, but if you have a heated garage, or live in a warm area (I didn't catch where you live), let it dry for as long as you can (you can even put a few 5000 watt lamps facing it, but dont cook it). After it is dry as you have time for, look for and make sure the engine mount holes are sealed, any other holes near the transom on or near the transom are sealed, and check all areas for compromised gel coat and make sure to seal them as well.
I use a good quality silicone for sealing around engine mount bolts and depth finder attachments. (I usually fill the hole with silicone before I instert the screw for depth finder attachments). Just make sure you clean the area with solvent (Rubbing alcohol, Toulene, MEK, or naptha will all work) then put it on and smear it. For sealing around the drain plug hole I would use a waterproof epoxy resin, this can be applied on the compromised gel coat as well.
Hope this helps,
"Ribbed, for her pleasure"