Why am I failing to sharpen my WÜSTHOF Classic Ikon 8" Cook's Knife, on my Shapton Glass Stone 1000 Grit 5mm?

It looks to me like a three--fold problem

1. The angle is constantly changing.

2. The action is bi-directional. You should only push.

3. You need to push the knife at about 45° to the direction of travel so you offer up the entire blade in each sweep, rather than just one end of it at a time.

oh, & a late 4… I don't think 1000 grit is going to be coarse enough to get the edge back on it once you've badly messed it up. I think you'll need 400 or so to get it back in the ballpark before refining it.

Having been rubbish myself at this for years, I'd honestly either give up now & get a decent electric, or at least try an angled clamp at the correct angle for a euro knife, 20°.
I also really really would advise against practising on a good knife.

Some images of blade edge profiles.

These are all "correct" profiles for different usages… however, let's just look at the top row first.
You really want one of the compound bevels [I think centre is Japanese, right is European]. To achieve these by hand you need some serious skill & practise. The best you'll really get is going to be closer to the V, if you're good &/or have a clamp system.
What you probably have right now is something closer to the convex on the 2nd row. In the right circumstances this could be a good thing [bushcraft or an axe-head]. In the hands of someone like me, it will barely cut cheese, let alone a soft tomato.
There is a lot of remedial work to be done to get back to one of the top row profiles.

I used to make knives and I agree with Tetsujin on all his points.

In short, to fix the problem you're going to need to reduce the variability of angle and use something coarser. That means a different type of sharpener.

I like carbide sharpers like this because they're fast and durable. But I also have a couple of ceramic sharpeners, including one by Kitchen Aid, that are so bad they aren't worth keeping in the drawer. I even have a knock-off of a Lanskey sharpener that's also really bad. But as long as you have one that will give you a consistent angle, even a cheap one will reduce error will give you better results. Even a $9 one.

As for grit, let me note this. When I visit my mom's, I'll sharpen her knife with a stone. But I have a lot of practice and the stone is about 200 grit. At around 600 grit, the metal starts to not just shine but reflect like a mirror. So your 1000 grit stone is going to take off very little metal, which is good because your grandfather's technique is bad.

Now, on the plus side, if you want to make your grandfather feel good, get one of the other sharpeners (read: carbidde), let him use it first and then "finish it off" with the stone. Unless he starts sawing on it, he won't do much with but the knives will still end up sharp from the first action with the carbide sharpener.