Rosemary extract can have antioxidant benefit for skin, but its aromatic components can cause irritation or sensitizing or toxic reactions on skin. When rosemary extract is present in small amounts it is much less likely to be a problem.

Rosemary extract is much less of a problem for skin than rosemary oil because the extract usually doesn’t contain much, if any, of rosemary oil’s volatile fragrance components.

Research has shown that rosmarinic acid, one of the components in rosemary extract, has a calming effect on skin, which may be useful for mitigating several common skin issues. Rosmarinic acid is an antioxidant, as is caffeic acid, another naturally occurring component of rosemary.

It’s also anti-microbial, and sometimes used as simply a fragrance ingredient.

References
Journal of Agricultural Food Chemistry, October 1999, pages 3954–3962
Chemical Research in Toxicology, November 2001, pages 1546–1551
Pharmacognosy Review, January-June 2014, pages 52-60
Journal of Medicinal Food, April 2013, pages 324-333
Chemical Research in Toxicology, November 2001, issue 4, pages 1546-1551
Journal of Agricultural and Food Chemistry, September 1999, issue 10, pages 3,954-3,962