osu! (specifically the stable version, as well as osu!lazer) allows players to manually define custom resolutions beyond the standard options (e.g., 1920x1080, 1366x768) displayed in the settings menu. This is a popular technique among competitive players to modify gameplay feel, reduce input lag, or force unconventional aspect ratios.
osu!lazer (the new, upcoming default client) handles resolutions much more elegantly. It does not require editing config files.
osu! stable stores resolutions in the configuration file, not the in-game dropdown.
This question pops up in the osu! community frequently. The answer is a definitive