I guess it's technically Vimeo's fault that it doesn't work on my phone, or maybe it's my Samsung phone's fault--I'm not sure. But it didn't work, and the error message just told me there was a problem and not how to fix it. Here's my Android test app, if you'd like to try it yourself. Click the link from your Android phone and follow the instructions.
Interestingly, I tried it on iOS and the video worked. But that's no surprise considering Apple's embrace of HTML5 and the "app" on an iPhone is an HTML5 page anchored to one of the iOS home screens.