Is there a genuine volume booster app for unrooted Android phones?

yes.

download POWERAMP music player.

it’s free version is very good to boost the volume and it’s pro version is awesome.

features of poweramp are:

plays mp3, mp4/m4a (including alac), ogg, wma*, flac, wav, ape, wv, tta, mpc, aiff

10 band optimized graphical equalizer for all supported formats, presets, custom presets

separate Bass and Treble adjustment

stereo eXpansion, mono mixing, balance

crossfade

gapless

replay gain

plays songs from folders and from own library

dynamic queue

embed and standalone .cue files support

support for m3u, m3u8, pls, wpl playlists

OpenGL based cover art animation

album art downloading

highly configurable widget types

visual themes, downloadable 3rd party skins available on Google Play

configurable lock screen

headset support, automatic Resume on headset and/or BT connection (can be disabled in settings)

tag editor

fast library scan

scrobbling

lyrics support, including lyrics search via musiXmatch plugin

high level of customization via settings

works on Android 2.3+.