Is this the dementia progressing?

There is a condition called esophageal stricture. It's where the throat muscles get tighter (constricted) and the esophagus (food tube) gets smaller and smaller. The food has no where to go and is usually brought back up by gagging.
A dilation (widening) is usually performed with a tube down the throat to open it back up but has to be done under sedation.

I certainly am not insinuating that your father is/was a drinker but this condition is very common in alcoholics. My dad was an alcoholic and he had many dilations in his later years.

Has he had his evaluation yet?

I agree with caregiverology, your dad needs a swallow evaluation by a speech therapist.
If your dad is having a hard time swallowing "thin" liquids (water, broth, anything that's easily pourable) and he's coughing afterwards, you may need a thickener.

There's a product called Thick-It that you can add to any liquid and it will thicken it to whatever consistency he'd need. It's available without a prescription. I got Mom's on Amazon. There is no flavor to the granules.

But, by all means, have him evaluated because aspiration pneumonia (a pneumonia caused by inhaling/choking on liquids or food and it gets into the lungs) is a further assault to an already weakened body.

Read up on the stages of Alzheimer's either here or Alz.org. His changes seem consistent for end stages of the disease. I'm sorry. My mom is there too. It's so hard to watch. ((hugs))

If his symptoms started about ten years ago, then the disease is not really progressing unusually fast. For many people with dementia the final, most severe stage comes by year ten or earlier. Others, especially with ALZ, may live with the disease longer.

Each individual case is different.

Your dad's ability to walk has probably been declining for some time. How long has be been using a cane, for example? It isn't a case of being able to walk with no problems at all on Monday, and needing a wheelchair on Tuesday. It may seem shocking when it finally reaches the wheelchair point, but it didn't happen overnight.

The swallowing difficulty has probably also been more gradual than you noticed.

The symptoms that are very noticable depend on what region of the brain is under attack. In some forms of dementia, the progression from one area to another in the brain follows a predictable pattern. In others it seems somewhat more "random," In some cases the progression seems extremely rapid and in others the decline is seems much more gradual.

Here is a short video showing how ALZ progresses. https://www.youtube.com/watch?v=Eq_Er-tqPsA

Other forms of dementia progress in different patterns, but they all progress (get worse). For example, in LBD the defect in the brain is not plaques and tangles but instead "bodies" of a mutant protein. In ALZ the part of the brain where hallucinations occur is impaired fairly late in the disease. In LBD that region is impaired early, and hallucinations might be the first noticeable symptom.

I think the general answer to your question is "Yes, this is the disease progressing."

My mil complains of having a sore throat, but with her hx of having her throat "stretched" over and over, I thought it might have been associated. I have mentioned it to her dr. and any one I thought would listen, but so far, nothing. Seems that nobody cares or wants to hear about it.

It sounds like he needs a consult for speech therapy to come in and evaluate his swallowing abilities. They will help determine what is causing the issue and will know how to proceed. It could be a number of different reasons. More than likely, they will put him on a special diet and possibly thickened liquids to start with. Dementia can progress extremely quickly in some cases. It's hard to say if that is what is affecting his throat or if it is something else entirely. Just be cautious because not only could he choke, depending on the circumstances, he could also get aspiration pneumonia hence the possibility of an order for thickened liquids. Best of luck.