Instead of “vertical” say that it’s laid out in “portrait” mode on the card instead of “landscape”. More people will know what you mean then, I think.
The bartender may have had other reasons than the appearance of the card to deny entry, or he may have been bad at math, or he may have just been too busy to even do the math (except don’t most places that serve or sell alcohol have signs that “your birthdate must be earlier than today’s date in [today’s year – 21]”?
I can’t imagine all of the reasons that people have for screwing things up. They’re so gosh-darned imaginative in the ways that they do that!