I've seen a few posts about replacing the glove box latch, I think it's going to be a similar issue on a number of the ML, GL, and GLK series SUV's so I decided to do a quick write up of how I did it.
* Remove the glove box, there are plenty of write ups on this so I'm not covering it.

View of left side of broken latch

View of right side of broken latch
* Carefully cut the tab on the left side of the latch and the 2 screws on the right side of the latch
* Press the tab that holds the glove box lid closed to create room to remove the cut screws and clean up with a vacuum
* I used gel super glue, but any all purpose epoxy will work. Put a few small drops of epoxy on the face of the vinyl, and plenty around the 2 posts of the new latch where the screws would thread into. Press the tab that holds the glove box lid shut and make sure the lever on the new latch is oriented on the left side to compress the slide mechanism when pulled and install the new latch.
* I pulled back some of the vinyl cover to see what was behind it so I used a bit of the glue to hold it back in place and taped it up, but that was not necessary overall.

Behind vinyl cover, not necessary to pull back to perform this repair. The post in the middle is what you need to make sure the lever of the new latch is able to press when installed.

I put a few drops of glue along the right side of the depression next to the holes the screw posts go through.

New latch installed, just need a new lock cylinder, but mechanism works as it should.
* Re-install glove box and get endless praise from your GF.