At first I thought Pokemon Go is the only issue, but today I installed Clash of Clans and it is the same situation: the game audio will try to go out through the Bluetooth channel but since there is no bluetooth device around, it is all mute.
If I plug in the earbuds, then I can hear something for both Pokemon Go and Clash of Clans. The other way is: if I find and turn on a portable Bluetooth speaker, or if I go to the car and use the bluetooth there.
But there should be a way to make these app go out through the iPhone's internal speakers. How can it be done? (if I turn off Bluetooth on the iPhone, it doesn't solve the problem).
P.S. the iPhone Music app doesn't have this problem. Only the apps do — so I don't think it is apps' problem. I am using iOS 10.2.1 which is quite recent.
P.P.S. just as a test, I just installed Angry Birds Rio, and it is exactly the same with Pokemon Go, Clash of Clans: no audio. So I don't think it is the apps' problem.
Best Answer
This is a bit of a guess based on an assumption I am making (dangerous, I know).
My assumption is that when you're playing games such as Angry Birds Rio that the audio is not actually outputting via Bluetooth at all.
Instead, I think the reason you do hear it when switching on a Bluetooth speaker is because at that point the iPhone starts outputting via Bluetooth. Prior to that, I think your iPhone is outputting via the iPhone's internal speakers but you're not hearing it because the volume level is not up for games.
What I mean is that iPhones have multiple volume levels. For example, it is possible to have the ringer volume level all the way up while having the games audio level all the way down.
As a test, I would start playing one of the games and make sure the volume is turned up (and also that the mute switch is not on). If that solves the problem, great! If not, report back so I or others can dig deeper.