IOS – Game sounds won’t play on iPhone 6

I would first check to see if the silent switch on the phone, above the volume buttons, is active. That would cause the issue. If that's not the case (the switch is off), I would try powering the phone down (hold down power button at top, then slide to power off), then restarting it.

If you can avoid bumping the sleep/wake button, you should have hours of playing time using AirPlay. Once the screen is dimmed due to a time-out, you can press sleep/wake to show the current track, just avoid pressing it to force an immediate sleep/screen dim. Let the timer do the work to ensure music playback.

I have Auto-Lock set at 5 minutes (with no passcode lock) and often set down my iPhone on the counter or place it in my pocket while I walk around the house, playing music until a low battery warning pauses playback. If you have to, shorten this setting during the party to avoid uncomfortable musical silences.