Think of the ending -er as a label you can stick on anything: the one that does this. Stick it on fight and you get the one that fights. Everything else follows from what you stick it to. Stick it on a person in a ring and you have an athlete. Stick it on a person in a war and you have a soldier. Stick it on a small quick plane and you have the machine that goes after other planes. Stick it on a game and you have the genre. Stick it on someone facing a hard year, and the fighting is no longer literal at all.
From the word’s history
The evidence packet records fighter as Middle English fightere, feghtere, from Old English feohtere, and analyses it as fight plus the agent ending -er. The modern uses are all that same formula applied to different things.
來源資料記載 fighter 來自中古英語 fightere、feghtere，再往前是古英語 feohtere，構造上就是 fight 加上表示「做這件事的人或東西」的 -er。今天的各種用法，都是同一個公式套在不同對象上的結果。
Wiktionary entry for fighter, etymology_text supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:282648058:58474)
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