Zooming in on the photo, they look unused. It looks like the edges flair out, which is how you put it on the bottle before you press it onto the bottle.
I would imagine that it wouldn't be difficult to press used caps back into a useable shape, but you then have to wonder if they are clean and not too weaked by use.
There is also a rubbery seal (silicone?) on a lot of caps, and I'd be worried that the seal would be damaged in the recycling.
They look unused. I never thought of re-use, but I would assume that if you're just opening a bottlecap without much care for preserving the cap (like when they sort of get bent down the middle) you'd be deforming it beyond re-use. It needs to be able to form a uniform seal around the bottle opening when capped and any bend will prevent that.
Never thought of trying out some bottle caps I tried not to damage when opening because they were pretty though.
Hot diggity dog. You've living the dream. I can't get the closest brewery to answer my inquiry about buying fresh yeast, old hops, etc. they're friendly, but not that helpful. A yes or a no would be sufficient.
I think that they will no longer sell beer in glass bottles with these caps. Best way to package beer is in kegs, bottles take too much time and efort to make.