An amusement gallery was a place of recreation.

In 2267, Spock claimed that a crewman stationed on Psi 2000 who was found dead with a phaser pistol in his hand had used the computer room as if it were an amusement gallery. (TOS: "The Naked Time")

Judging by the context this term was used in, it would seem to indicate that "amusement gallery" is synonymous with "shooting gallery", and therefore, the crewman used the room for target practice.
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