Take shoot and hang -er on the end: the one that shoots. English lets that one be a person, a thing, or even a whole kind of game. So when you meet shooter, the useful question is not what does it mean but what is being shot here — a bullet, a ball, an arrow, or a camera shutter. The sentence around it almost always answers that.
Wiktionary records shooter as Old English sċēotere, by way of Middle English schoter — that is, shoot plus -er. The one that shoots was the shape of the word from the start, and every modern use still runs along that line.
Wiktionary 記載 shooter 來自古英文 sċēotere，經中古英文 schoter，構造就是 shoot 加上 -er。也就是說，「射的那個」從一開始就是這個字的形狀。今天不管是人、是槍、是遊戲，都還照著這條線走。
Wiktionary (kaikki extract, source_ref kaikki:3f6f69a190036ae4:1157268343): "From Middle English schoter... from Old English sċēotere (shooter), equivalent to shoot + -er."
From the picture
射的那個東西
-er 不一定指人，也可以指工具。同樣是「射的那個」，只是這次指的是手上那把東西，所以 shooter 就成了槍的口語說法。
noun · B2
An informal word for a gun. You meet it in speech and in tough-talking films and stories rather than in reports or careful writing, where people say gun or firearm.
槍（口語）
以射為主的遊戲
這次 -er 掛到的不是人也不是工具，而是一整段活動：這款遊戲從頭到尾主要在 shoot，所以遊戲本身就被叫做 shooter。
noun · B1
A video game in which shooting at enemies or targets is the main thing the player does. It also names the whole type of game.
射擊遊戲
noun · B1
A person who shoots — most often someone firing a gun, and also someone using a bow. It simply names whoever is doing the shooting, in a sport, in a report, or in a story.
射擊的人
noun · B1
In basketball, a player who is good at throwing the ball through the basket, especially from a long way out. Used mainly in American English.
射手（籃球）
noun · B2
An informal word for a photographer or camera operator, used mainly by people who work with cameras.
攝影師（行話）