With the exception of the Oxford English Dictionary and several others, of course.
This is false. As you have just acknowledged in your own comment.
The OED has multiple on record in major print publications examples of use of the word american in multiple contexts. One of those is specific to the United States of America which is the more common usage.
Not the only, and not always unambiguously so.
I didn't acknowledge that. Instead you told me to check the dictionary which is not at all relevant to what I said. If somebody holding a dictionary came up to you and told you they're American, would you assume they meant they're from the US, or somewhere across two vast continents? Which is more likely? I think you know the answer even if you want to be pedantic about it.