I'm not familiar with the term dog hole. You mean like what is shown in this image?

What is the purpose? How is that you did accidental?

I think that would be a perfectly good jaw vise. But only put in a few dog holes, as shown in their product photos, to maximize rigidity.

Man, this is some confusing perspective material. I thought, the holes protruded outwards, like a halved bottle cork. I just didn't get at all, how they could be at such weird angles...

Personally I would go with some hardwood for the vise jaws. The plys can have voids and you a removing a lot of material from the sheets. If you can't get a piece of hardwood thick enough just laminate 2 together.

Paul Sellers has been known to use plywood jaws in years past, but he is using some nice stuff with a lot of void-free plies, and he is not putting dogholes in it. Honestly, though, even the material you have there, if laminated to 1.5" and with just one or two 3/4" dog holes, it should work pretty well and would be easy to replace. If you are on a budget but want to do hardwood, this is a perfect job for red oak.

Depends on the type of work, but you may want something denser down the road if you find you're cranking down on a narrow piece and it's flexing. Even something with more plies like Baltic birch might give you more mass, but I've only ever used hardwoods for my vises so can't say for sure.

Also recommend those cork/rubber jaw liners for added grip.