In Options, turning on Windowed mode, moving the Resolution slider, it asks to Press A to Apply. Whether I press 'A' key on the keyboard, or press the letter A on the screen using the mouse, or pressing Enter, the resolution does not change. I tried quitting and starting again, but the window fills up almost the whole screen.

Well, here is a solution I found.

1. Quit the game

2. Edit the file ~/.config/unity3d/Night\ School\ Studio/Oxenfree/prefs and manually change the resolution for the following entries:
<pref name="Screenmanager Resolution Height" type="int">768</pref>
<pref name="Screenmanager Resolution Width" type="int">1024</pref>

3. Start the game