Seems correct. See the refs.

Real-time strategy game is fine in my opinion (real-time as opposed to turn-based).

Check out Wikipedai's definition:
Real-time strategy (often abbreviated as RTS) is a genre of computer wargames which take place in real-time, where resource gathering, base building, technology development and direct control over individual units ("harvest, build, destroy") are key components[1], which distinguishes it from related strategy wargame genres, such as turn-based strategy and real-time tactics.

Real-time strategy titles do not involve "turns" like turn-based strategy video or board games (such as chess). Rather, game time progresses in "real time". It is continuous rather than turn-by-turn and all players may interact with the game environment at any time. This is in many cases a very distinct form of play, as mere seconds of distraction could give the enemy an advantage (contrasting to turn-based where the opponent cannot counter until the player is done). While the word "strategy" originally referred to high-level war planning of armies, campaigns, and entire wars (including logistical concerns such as economy and unit production), in real-time strategy games it is possible to give orders to individual units or persons. So, for some more recent games it might be more appropriate to call the gameplay "tactics" or "strategy/tactics hybrid".