Regarding Lunar Lander and Spacewar, the story goes that DEC commissioned the GT40 graphical version of Lunar Lander explicitly to repeat the success of Spacewar as a demo application. If true this showed that both programs were in the same category, which may be rather “entertaining simulation” than “game”.
There’s a prehistory to this, since similar simulation setups, like displaying missile trajectories, bouncing balls, etc, came previously as demos with analog computers. Notably, Higinbotham’s “Tennis”, AKA Tennis for Two, was essentially a mashup of such physics simulations. – As this thread shows quite well, it’s hard to separate simulations from early games.
As for graphical physics simulations, Bouncing Ball (Charles Adams, Whirlwind, MIT, 1949) has its well deserved place in computer history.
Similarly, Michigan Pool (William George Brown and Ted Lewis, MIDSAC, 1954) deserves a mention as an entertaining physics demonstration serving as a stand-in for the classified application, which normally ran on the computer, solving guidance problems similar to computing the trajectories of the balls in “Pool”.