Ok, on my model, GX631GW I had the exact same problem.
The keyboard was stuck to the battery and when I was trying to remove the keyboard it was lifting the battery up as well, right in the middle of the laptop.
After getting it apart I couldn’t find any trace of an adhesive or double sided tape.
My guess is that the standoff that is embedded on the keyboard side gets stuck inside the opening in the battery frame.
The easiest way to free them is to start by going to the left side of the laptop, prop the two parts apart just far enough so that with a light you can inspect the inside.
Verify that your laptop is stuck at the same point as mine!
Then, with a long, thin, plastic tool, wedge between the standoff and the battery frame and twist to push them apart (imagine twisting a flat head between two surfaces, it should cam and push the two apart).
Then continue on to the next steps in the guide.
This is a crucial step, ensure that you don’t snag the ribbon cables at this point because parts can be difficult to get.