That would be Choki style Karate, developed by a contemporary of
Gichin Funakoshi, Motobu Choki. Many Japanese familiar with the
Choki style, in fact consider it more practical than Shotokan,
since its movements are not as expansive, and the Kata emphasize
simplicity and efficiency rather than "showy" and "big" motions. It
may be of interest to you, that Choki was a street brawler, and he
had the same mentality as Bruce Lee; Motobu Choki felt that most
Okinawan Karate "did not work on the street" so he developed his
own out of his own street brawling experiences. Long before
Masatatsu Oyama and his Kyokshin, there was Motobu Choki.