Burger without patty?

If you order a burger, it should definitely come with a patty made up of ground beef. In some cases, the burger could be made of chicken, turkey, bison, etc. But, in that case the type of meat is generally specified. In the case of beef, the type of meat is generally ommitted from the details, and assumed the patty will be beef. Here is a picture of what you can expect to get if you order a "burger" in America.

I have never heard of a burger that comes with squares of salami instead of a ground patty of some kind. It's possible to have a ground pork burger, but not salami. It seems to me what you were serves is best considered a "salami sandwhich".

The wikipedia article you linked describes "a sandwich consisting of one or more cooked patties of ground meat, usually beef, placed inside a sliced bread roll or bun." right at the beginning.

Unless regional differences apply, if there is a definition of a dish that is undisputed enough to be publicly documented in this way, one can assume that it is a restaurant's duty to clearly tell you about their different interpretation (on the menu or by telling you upon ordering).