From what you have written here my best guess is that she is bored and depressed. You stated that she is remembering and still able to play games just with drawing. Even though withdrawing is a sign of both depression and dementia, without any other symptoms my guess would be depression.
You could do an online search for a MMSE (Mini Mental Status Exam). It is a series of 30 questions that you can ask. If she gets all of them, or even most of them right then it is more likely depression. Some of the other things you can look for is repeating herself. Does she tell you a story and then repeat that story a few minutes later? Does she still know how to use the TV remote or cordless phone? Can she follow complex instructions with multiple steps? Does she accuse people of doing things when in fact she was the one that is responsible? Many times they will put away things and forget where accusing family of stealing. Can she still do math? Dementia patients will lose the ability to think in the abstract which math involves. Can she still put together jigsaw puzzles? Dementia will damage the spacial thinking early and they will lose the ability to manipulate the puzzle pieces and know where to put them.
Her fear of falling is obviously warranted due to the weight and the falls. Grandpa's nagging doesn't help. I see this as a logical reaction. You also need to know that because she is not active, the calorie intake, though greatly reduced, is probably sufficient to maintain her body weight. It doesn't take much. But you are right that not using her ability to ambulate will cause her strength and ability to ambulate to decrease.
My best suggestion to you is to take her to her doctor and have a conversation with him making sure he understands what is happening with her. You might even want to talk to him first so he will be aware before the exam. She needs a complete physical, with blood work, and he needs to do the MMSE with her to check her cognitive abilities. If it is depression then there is medication that may help. I would also suggest that you request a physical therapy evaluation. Especially if she is cognitively well, they will be able to help her feel safe again.
I hope this is just depression, based on your words here, but please take her to the doctor and find out for sure