Mine is locked away right now, bbut I am pretty sure it is a simple bi-fold card that would be stamped r signed by the AD with the date of purchase and probably the watch serial number on it. In any case, it is what needs to be presented with the watch when you send it in for repair under warranty. If you cannot get it from the seller, perhaps you can follow up with JLC to get a replacement, although I have never done that so I am not sure whether they will do that or not.
Hope that helps.
In the meantime, enjoy your watch. It is an awesome JLC. Yes, it is on the cusp of being a weekend AND weekday watch, but I think you are right it is pretty sporty and one might not feel comfortable wearing it for business. One of the things about the AMVOX2 DBS is that it is quite unusual and I think that may make it difficult at first to figure out where and when to wear the watch. But you will sort that out in due time.
I notice you have it on a different strap that the one that is typically issued with the DBS. Do you have more photos to share?
Cheers,
respo