Alsa only applications support
Most applications on Alpine Linux are compiled to support only ALSA, foregoing linking against libpulse and the ability to dynamically switch to pulseaudio output when it finds that pulseaudio is running. Install the pulse output plugin for ALSA so applications can output to Pulseaudio.
Pulseaudio should run with an elevated priority, because e.g. crackling or delayed audio is more annoying than a low framerate in games.
Installing the shadow package (which is compiled against linux-pam) is an easy way for the non-root user to be granted the ability to change niceness, and pulseaudio is recommended to be run as the user, rather than as root. E.g. in /etc/security/limits.d/audio.conf (and putting the user in the "audio" group):
@audio - nice -11