Yep, that's a sneakbox transom. ....Well, if it were me I would go to Beaton Bros in Mantaloking and have them build me a proper cedar on oak one. Lol
Ok, it's a little transom, pretty simple job. I'd probably flip her over on saw horses to make getting in there easier. Take a cheap 'beater chisel' and mallet to cut through through the glass around the edges and just keep going at the ply, taking it out in pieces. Shouldn't take more than a couple of hours. Then make a pattern from the inside (can use a couple of brown paper grocery bags cut open & taped together). Or for this, even just trace the outside and then reduce the size about 1/2 to 3/4 all the way around. When you like the fit, glue it in with thickened epoxy. A sneak box is so small you could probably even stand her on her transom against the house to make it easy to just put weights inside on the transom (stack of concrete block, etc) to 'clamp' the transom while the epoxy sets.
Really an easy little project. Good luck.