There are several uses for "Role-playing" besides that used in the LARP, table-top and computer games.
In Social Work, Psychology and Psychology, it's done as a guided theraputic technique, with almost no use of props nor of randomization, rulesets, nor even written characters. Usually in the mode of, "Fred, pretend you are Joe. Tell me what you think of Fred." If the responses become in need of adjudication, usually the exercise is usually stopped, or some predetermined outcome is used.
In Education, the term is avoided, but the same technique is often used in enrichment activities, but to explore historical persons rather than persons one is in conflict with. Some simulations are in fact highly structured low-choice RPG's; some even use dice or spinners as randomizers. Mock Trials in civics classes are in fact roleplaying; they are a longstanding tradition in social studies education.
In board games, "Role-playing" means either speaking in character, or playing a single character with some activities resolved by methods that don't involve the main game board. Several games have role-playing as a mode of play, but are clearly not RPG's.
In computer games, it generally means a game with a strong story element, and players controlling one to six individually statted characters, usually acting as a single player; the relation to tabletop RPG's is in mechanics of combat and advancement more than in mode of play. The games sharing the mode of play are called, generally, "interactive fiction" rather than "role-playing"...
In Theater, Improvisational Acting ("Improv") is sometimes termed role-play acting, tho the term is not standard; sometimes, it's done with assigned character aspects. It can be very much like LARP in many cases. The distinctions between improv and LARP, and between improv and diceless games is one of degree and decree... the later meaning that in diceless games and in LARP, there is someone with authority to resolve issues.
I have seen documentation of the use of Role-playing simulation excercises in both Business and Poli-Sci collegiate courses. It often uses random elements. The most common is the stock market investment simulation; the students write their buy/sell orders on day A, and on day B resolve them with A's close prices; they often are allowed to buy/sell in-class, as well.