I'm having a similar problem on one of my more sensitive vines.

I hope it's not a herbicide overspray?

I don't think it's herbicide. Herbicide damage usually causes stunted yellow/white growth.

What variety are they?

Did you spray them with anything? Sulfur and copper can burn leaves depending on the variety. Usually is only on the edges of the leaf where the material would stay for a longer time before drying. So, maybe not...

In the second photo I see the small new shoot is dying so I'm thinking a fungal disease.

My best guess would be angular leaf scorch, but it doesn't look quite like that either...

Powdery mildew and downy mildew can make the young growth shrivel like that, and eventually make the leaf brown.

What do the other leaves/plants look like? Anything with less advanced stages of the problem?

The variety affected is Glenora, my two plants of Glenora have this condition while the other six plants I have in other grape varieties do not exhibit it at all and look fine. I did not spray them with anything.

Should I remove these plants from my vineyard and replant in a different variety?

I too grow grapes and none of mine look this. This will be a dumb question but any insects on the backsides of the curled leaves? Just asking as this year my rhubarb in the past week had all the newer and young leaves curl up just like your glenora grape leaves. Some are now dying. Never had the problem before. It turns out the young leaves are just coated with some sort of sucking insects on the undersides of the leaf. Sprayed Malathion on them last night. I never had any insect issues on rhubarb before.

I too would guess some sort of fungal issue on the grapes but weird that the last photo shown shows such a puckered up leaf (just like my rhubarb has).

I wouldn't remove the plant, unless you don't like Glenora, removing the effected tissue would help cut down the inoculum present if it is fungus.

Some varieties are more susceptible to disease than others. Glenora is listed as highly susceptible to powder mildew. If it is powdery you may see it on the berries.