Is "liberal arts" a unique feature of American higher education?
It's probably not unique, but practically yes the concept of a "liberal arts" college or education is specific to North America. Some European countries have a form of "liberal arts" curriculum at the high school level (e.g. the German or Swiss Gymnasium) where a broad spectrum of "classic" subjects are taught with the purpose of allowing students to join any university education.

But (continental) European universities generally have individual programs for math, philosophy, history, science, etc.

It's actually quite puzzling for people who attended university in Europe to hear their US-educated colleagues say "Yes, I majored in physics and medieval music".