"Sunt românești" is "They are Romanian," because "românești" is the plural form of the adjective.
In order to be "I am Romanian," it would have to say, "Sunt românesc," (for a male speaker) or "Sunt românească" (for a female speaker).
I'm romanian is Sunt român for man and sunt româncă for female. românesc or românească is used to refer to things exemplu: the car is romanian, mașina e românească.
I hear tromânești in slow version especially.