I know technically any file explorer app can do that. Browse to your music folder, select track file, it'll ask for which player to use, doesn't matter which one, they all will play it once and stop. Some file explorer has built in player that show a small pop up and play right there but if touch outside that little windows, it will exit play.
So I test a bunch of file explorer apps and found the best one for this purpose is AntTek Explorer Ex. Still has built-in player but full screen interface like google play music so no worry about accidently touching screen and exit play, no need to jump back and forth to another app, more seemless playback, auto go back to track list once play ended. No ads too & nice interface!
play.google.com/store/apps/details?id=com.anttek.explorerex
Another option is Music Folder Player Free by ZorillaSoft, not very nice looking, but works. make sure go to settings > behavior > Musician mode (auto pause playback at the beginning of the next track) is checked.
play.google.com/store/apps/details?id=de.zorillasoft.musicfolderplayer
