Swag as slang-
Swag, slang originating in the early 1800s for stolen goods or booty; possibly carried by a swagman
Swag, slang originating from the Scottish slang word "swagger" which was a description of the way some Scots walk (in a swaying motion). The word was altered in the English language to mean "the way one presents oneself".
Swag, promotional items given away at trade fairs and events
The phrase "He/She has swag." only makes literary sense if taken as follows: "He/She has (a way to present oneself as an individual)."
Other uses-
Swag Stick, a
short cane carried by a military officer.
Sources: Websters
Dictionary and
Wikipedia.