I connect my xbox 360 to active speakers and youtube app has no volume control! I think volume is 100% by default! are you crazy? this is terrible, because it's TOO LOUD on some videos with high sound level
The RCA-type outputs from the Xbox 360 are at standard line level. The output is the same as a CD player, DVD player, or any source device. The problem is not the YouTube app. The problem is that your audio system doesn't have a volume attenuator control.
The solution is to get a stereo or active speakers that have a volume control. There are many options. One of the more cost effective compromises is to look at active recording studio speakers in music instrument shops, or online used sales like Craigslist
or Kijiji. They can be inexpensive and sound decent, and you'll have full control over the volume.