Looked at the pictures you added and it appears that a previous owner may have tried to saw away some debris out of that joint, hard to tell but it looks like a cut edge on one of the vertical panels. After re-gluing the cabinet, it may require some filler. I've had good luck with Sherwin-williams resin based patching compound for items like this. Also, you should do something about the hole that is used for the speaker leads. These openings are not letting you get the optimum sound from your Altec's. If I could find it, I'd put up a link to the paint that matches the original VOTT grey, but I can't seem to locate it.
Good luck with your Altec's and welcome to the Forum.