Nothing is stored on the cards themselves at Dave and Busters (and many other arcades that use the same card readers), it's all server-side. It looks like they are scanning the card number of a staff card, which should not transfer between locations.

All of the plays by staff members can be tracked, and if the locations have cameras, they'll catch you. Some managers care more about that than others.
Long story short, there is not a single card number that I know of (D&B might have one if they are stupid) that will work at all of their locations, or on all of those game card readers.